GB2642294A

GB2642294A - A system and method for time transfer

Info

Publication number: GB2642294A
Application number: GB2409425.2A
Authority: GB
Inventors: Page Carlo; Koehler-Sidki Alexander
Original assignee: Arqit Ltd
Current assignee: Arqit Ltd
Priority date: 2024-06-28
Filing date: 2024-06-28
Publication date: 2026-01-07
Also published as: WO2026003481A1; GB202409425D0

Abstract

System for time transfer between a first and second clock, comprising an entangled photon transmitter 100, a first photon receiver 200 comprising first clock 600, and a second photon receiver 300 comprising second clock 700. Entangled photons are generated and first 114 & second 116 photons are transmitted to the respective receivers 200/300. At the receivers 200/300, respective series of emission timestamps are determined by removing respective time of flight offsets from each detection timestamp. A clock offset between the first 600 and second clock 700 is determined by calculating a cross-correlation between the respective series of emission timestamps, and time is transferred by adjusting either clock by the clock offset. A group clock offset may be determined from an average of a plurality of clock offsets, and the clocks may be adjusted by the group clock offset. The transmitter 100 may be at a satellite. The time of flight offsets may be determined using a synchronisation laser system or a laser ranging beam.

Description

[0001] A SYSTEM AND METHOD FOR TIME TRANSFER

[0002] The present application relates to a method, system and software for time transfer. Background [0002] Cryptography is used to protect billions of transactions every day from, without limitation, for example Transport Layer Security (TLS) security for online shopping and banking to ultra-secure government communications. These transactions rely on reliable and secure means for at least two or more transacting parties to share a secret key, enabling encryption of data by one party and subsequent decryption by other parties.

[0003] It is expected that when commercially usable universal quantum computers (QC) become available, a variety of types of transactions, tasks and applications including, without limitation, conventional key distribution processes will be vulnerable. QCs can potentially crack many classical cryptography codes almost effortlessly. The conventional manual key distribution process is not quantum secure by its nature of operation, as it is exposed to both quantum electronic and/or physical compromise at several of the steps involved.

[0004] It has been proposed to use quantum key distribution (QKD) to allow two distant parties to share a key in an information theoretic secure way that is guaranteed by the laws of physics. Significant progress has been carried out in recent years on implementing this over fibre. However, the loss experienced over terrestrial links severely limits the achievable distance. By utilising the negligible loss experienced by photons travelling through most of the atmosphere, satellite based QKD can overcome these limitations and enable inter-continental QKD. However, in order to enable satellite based QKD an improved method for time synchronisation between a satellite and a ground station is needed.

[0005] The embodiments and arrangements described below are not limited to implementations which solve any or all of the problems of the known approaches described above.

[0006] Summary

[0007] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to determine the scope of the claimed subject matter; variants and alternative features which facilitate the working of the invention and/or serve to achieve a substantially similar technical effect should be considered as falling into the scope of the invention disclosed herein.

[0008] According to a first aspect, there is provided a method of time transfer between a first clock and a second clock, the method comprising: at an entangled photon transmitter, generating a series of entangled photons, wherein each entangled photons comprise a first photon and a second photon; at the entangled photon transmitter, for each entangled photons, transmitting the first photon to a first photon receiver comprising the first clock; at the entangled photon transmitter, for each entangled photons, transmitting the second photon to a second photon receiver comprising the second clock; at a first photon receiver, determining a series of first detection timestamps of when ones of the first photons were received by the first photon receiver; at the first photon receiver, determining a series of first emission timestamps of when the received first photons were transmitted by the entangled photon transmitter by: determining a first time of flight offset of each first detection timestamp; and removing the first time of flight offset from each first detection timestamp, at the second photon receiver, determining a series of second detection timestamps of when ones of the second photons were received by the second photon receiver; at the second photon receiver, determining a series of second emission timestamps of when the received second photons were transmitted by the entangled photon transmitter by: determining a second time of flight offset of each second detection timestamp; and removing the second time of flight offset from each second detection timestamp; communicating, the series of first emission timestamps to the second photon receiver, or the series of second emission timestamps to the first photon receiver; determining, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; transferring time between the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

[0009] According to an embodiment, the method further comprises: determining, a plurality of clock offsets by repeating steps of the first aspect for a corresponding plurality of series of entangled photons; determining, a group clock offset, wherein the group clock offset is an average of the plurality of clock offsets; transferring time between the first clock and the second clock by adjusting either the first clock or second clock by the group clock offset [0009] According to an embodiment, the entangled photons share temporal correlations when the entangled photons are generated by the entangled photon transmitter.

[0010] According to an embodiment, the entangled photons are a pair of entangled photons.

[0011] According to an embodiment, the first photon is an idler photon and the second photon is a signal photon.

[0012] According to an embodiment, the plurality of photons are entangled by time energy, polarisation, frequency, or time-bin.

[0013] According to an embodiment, determining the detection timestamp of when a photon was received by the photon receiver comprises: receiving the photon through a telescope; detecting the photon via a quantum receiver system; demultiplexing the photon from a sync laser; and recording a detection event of the photon with a timetagger.

[0014] According to an embodiment, determining the emission timestamps comprises performing a time synchronisation process to remove time of flight offsets for each photon receiver to calculate estimates of when each single photon was emitted from the entangle photon source.

[0015] According to an embodiment, removing the time of flight offset from the detection timestamps provides distance synchronisation between the first photon receiver and the second photon receiver.

[0016] According to an embodiment, the entangled photon transmitter comprises a synchronisation laser system and determining the time of flight offset comprises using the synchronisation laser system.

[0017] According to an embodiment, using the synchronisation laser system comprises: transmitting, by a photon receiver, using a telescope, a sync pattern to a retroreflector co-located with the entangled photon transmitter; returning, by the retroreflector, the sync pattern to the photon receiver; receiving, by a sync detector system, the sync pattern, wherein the sync detector system is co-located with the photon receiver by demultiplexing the sync pattern; determining, by the sync detector system, a delay in receiving the sync pattern to determine the time of flight offset [0018] According to an embodiment, the photon receivers comprise a time of flight ranging system and determining the time of flight offset comprises: transmitting, by the photon receiver, a laser ranging beam from the photon receiver to the entangled photon source, wherein the laser ranging beam is encoded with a predetermined pattern signal; reflecting, by the entangled photon source, the laser ranging beam as a reflected laser ranging beam; receiving, by the photon receiver, the reflected laser ranging beam; comparing, by the photon receiver, a transmitted time of the original laser ranging beam and a received time of the reflected laser ranging beam, based on the predetermined pattern signal, to determine a time of flight offset of the reflected laser ranging beam; and determining, by the photon receiver, the time of flight offset of the detection timestamp by halving the time of flight offset of the reflected laser ranging beam.

[0018] According to an embodiment, the first photon receiver sends the first time of flight offset to the second photon receiver.

[0019] According to an embodiment, determining, for each entangled photons, a clock offset between the first emission timestamp and the second emission timestamp is at the second photon receiver [0021] According to an embodiment, the second photon receiver sends the second time of flight offset to the first photon receiver.

[0020] According to an embodiment, determining, for each entangled photons, a clock offset between the first emission timestamp and the second emission timestamp is at the first photon receiver [0023] According to an embodiment, the second photon receiver and the first photon receiver communicate the first emission timestamp or the second emission timestamp via a classical communication channel.

[0021] According to an embodiment, the cross-correlation comprises identifying matched events between the first time of flight offset and the second time of flight offset, wherein the matched events are offset by the clock offset.

[0022] According to an embodiment, the method further comprises determining a variation in the clock offset over time to determine frequency variations in between the first clock and the second clock.

[0023] According to an embodiment, the entangled photon transmitter is located separate from the first photon receiver and the second photon receiver.

[0024] According to an embodiment, the entangled photon transmitter is located on a satellite; and the first photon receiver and the second photon receiver are optical ground receivers.

[0025] According to an embodiment, the second photon receiver is located separate from the entangled photon transmitter and the first photon receiver.

[0026] According to an embodiment, the entangled photon transmitter and the first photon receiver are located on a satellite; and the second photon receiver is an optical ground receiver.

[0027] According to an embodiment, the second photon receiver and the entangled photon transmitter are located separate from the first photon receiver.

[0028] According to an embodiment, the first photon receiver is located on a satellite; and the second photon receiver is an optical ground receiver, and the entangled photon transmitter is located on the optical ground receiver.

[0029] According to an embodiment, the clocks discipline the timing systems of the photon receivers.

[0030] According to an embodiment, the first clock is a child clock and the second clock is a parent clock, wherein child clock is adjusted to share a common time with the parent clock.

[0031] According to an embodiment, the first clock is a low quality clock and the second clock is a high quality clock.

[0032] According to an embodiment, the entangled photons are polarisation entangled or frequency entangled.

[0033] According to an embodiment, the method further comprises monitoring correlations in the polarisation states, or frequency, of the entangled photons.

[0034] According to an embodiment, the quantum bit error rate of the series of entangled photons are monitored, based on the correlations in the polarisation states or frequency, to detect intercept-resend attacks.

[0035] According to an embodiment, the method further comprises repeating steps of the first aspect to transfer time between the first clock or second clock, with a third photon receiver comprising a third clock.

[0036] According to a second aspect, there is provided a system for time transfer between a first clock and a second clock, the system comprising: an entangled photon transmitter configured to: generate a series of entangled photons, wherein each entangled photons comprise a first photon and a second photon; and transmit, for each entangled photons, the first photon to a first photon receiver comprising the first clock; and transmit, for each entangled photons, the second photon to a second photon receiver comprising the second clock; the first photon receiver comprising the first clock, the first photon receiver configured to: determine, a series of first detection timestamps of when the first photons were received by the first photon receiver; and determine, a series of first emission timestamps of when the first photon were transmitted by the entangled photon transmitter by. determining a first time of flight offset of the first detection timestamp; and removing the first time of flight offset from the first detection timestamp; the second photon receiver comprising the second clock, the second photon receiver configured to. determine, a series of second detection timestamps of when the second photons were received by the second photon receiver; and determine, a series of second emission timestamps of when the second photons were transmitted by the entangled photon transmitter by: determining a second time of flight offset of the second detection timestamp; and removing the second time of flight offset from the second detection timestamp; and the system being configured to: communicate, the series of first emission timestamps to the second photon receiver, or the series of second emission timestamps to the first photon receiver; determine, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and transfer time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

[0037] According to a third aspect, there is provided a method of time transfer between a first clock and a second clock, at an entangled photon transmitter in a time synchronisation system, the method comprising: generating a series of entangled photons, wherein each entangled photons comprise a first photon and a second photon; for each entangled photons, transmitting the first photon to a first photon receiver comprising the first clock; for each entangled photons, transmitting the second photon to a second photon receiver comprising the second clock; communicating, a series of first emission timestamps to the second photon receiver, or a series of second emission timestamps to the first photon receiver; determining, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and transferring time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

[0038] According to a fourth aspect, there is provided a system for time transfer between a first clock and a second clock, the system comprising an entangled photon transmitter configured to: generate a series of entangled photons, wherein each entangled photons comprise a first photon and a second photon; transmit, for each entangled photons, the first photon to a first photon receiver comprising the first clock; and transmit, for each entangled photons, the second photon to a second photon receiver comprising the second clock; communicate, a series of first emission timestamps to the second photon receiver, or a series of second emission timestamps to the first photon receiver; determine, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and transfer time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

[0039] According to a fifth aspect, there is provided a method of time transfer between a first clock and a second clock, at a first photon receiver comprising the first clock in a time synchronisation system, the method comprising: at a first photon receiver, determining a series of first detection timestamps of when first photons were received by the first photon receiver; at the first photon receiver, determining a series of first emission timestamps of when the first photons were transmitted by an entangled photon transmitter by determining a first time of flight offset of the first detection timestamp and removing the first time of flight offset from the first detection timestamp; communicating, the series of first emission timestamps to a second photon receiver, or a series of second emission timestamps to the first photon receiver; determining, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and transferring time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

[0040] According to a sixth aspect, there is provided a system for time transfer between a first clock and a second clock, the system comprising a first photon receiver comprising the first clock, the first photon receiver configured to: determine, a series of first detection timestamps of when first photons were received by the first photon receiver; determine, a series of first emission timestamps of when the first photons were transmitted by the entangled photon transmitter by: determining a first time of flight offset of the first detection timestamp; and removing the first time of flight offset from the first detection timestamp, communicate, the series of first emission timestamps to a second photon receiver, or the series of second emission timestamps to the first photon receiver; determine, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and transfer time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

[0041] According to a seventh aspect, there is provided a computer-readable medium comprising code or computer instructions stored thereon, which when executed by a processor, causes the processor to perform the method according to any one of the first aspect, the third aspect, and the fifth aspect.

[0042] The methods described herein may be performed by software in machine readable form on a tangible storage medium e.g. in the form of a computer program comprising computer program code means adapted to perform all the steps of any of the methods described herein when the program is run on a computer and where the computer program may be embodied on a computer readable medium. Examples of tangible (or non-transitory) storage media include disks, thumb drives, memory cards etc. and do not include propagated signals. The software can be suitable for execution on a parallel processor or a serial processor such that the method steps may be carried out in any suitable order, or simultaneously.

[0043] This application acknowledges that firmware and software can be valuable, separately tradable commodities. It is intended to encompass software, which runs on or controls "dumb" or standard hardware, to carry out the desired functions. It is also intended to encompass software which "describes" or defines the configuration of hardware, such as HDL (hardware description language) software, as is used for designing silicon chips, or for configuring universal programmable chips, to carry out desired functions.

[0044] The preferred features may be combined as appropriate, as would be apparent to a skilled person, and may be combined with any of the aspects of the invention.

[0045] Brief Description of the Drawings

[0046] Embodiments of the invention will be described, by way of example, with reference to the following drawings, in which: [0049] Figure 1 is a schematic diagram illustrating a satellite quantum key distribution system according to a first arrangement; [0050] Figure 2A is a schematic diagram illustrating a satellite based part of a synchronisation system according to the first arrangement; [0051] Figure 2B is a schematic diagram illustrating a ground based part of a synchronisation system according to the first arrangement; [0052] Figure 3 is an explanatory diagram illustrating some possible timing problems; [0053] Figure 4A is schematic diagram illustrating laser pulse sequences generated on board the satellite according to the first arrangement; [0054] Figure 4B is schematic diagram illustrating laser pulse sequences received at a ground station according to the first arrangement; [0055] Figure 5 is a schematic diagram illustrating a flow chart of a time correlation process by the ground station according to the first arrangement; [0056] Figure 6 is an explanatory diagram illustrating a correlation process carried out at a ground station according to the first arrangement; [0057] Figure 7 is a schematic diagram illustrating laser pulse sequences optionally generated on board the satellite according to a specific example of the first arrangement; [0058] Figure 8 is a schematic diagram illustrating a satellite quantum key distribution system according to a second arrangement; [0059] Figure 9 is a schematic diagram illustrating a system for time transfer according to a first embodiment of the invention; [0060] Figure 10 is a schematic diagram illustrating an entangled photon transmitter according to the first embodiment of the invention; [0061] Figure 11 is a schematic diagram illustrating a first photon receiver according to the first embodiment of the invention; [0062] Figure 12 is a detailed schematic diagram illustrating the first photon receiver according to the first embodiment of the invention; [0063] Figure 13 is a schematic diagram illustrating a second photon receiver according to the first embodiment of the invention; [0064] Figure 14 shows a laser ranging system according to all embodiments of the invention; [0065] Figure 15 is a time diagram illustrating true emission timestamps detected by the first photon receiver and the second photon receiver; [0066] Figure 16 is a time diagram illustrating detection timestamps of when the photons were received by the first photon receiver and the second photon receiver, including time of flight offsets and clock offsets; [0067] Figure 17 is a time diagram illustrating emission timestamps of photons received by the first photon receiver and the second photon receiver, including clock offsets for all embodiments; [0068] Figure 18 is a cross correlation output diagram illustrating the clock offset between the first emission timestamps received by the first photon receiver and the second emission timestamps received by the second photon receiver for all embodiments; [0069] Figure 19 is a schematic diagram illustrating a second time transfer system according to the second embodiment of the invention; [0070] Figure 20 is a schematic diagram illustrating a third time transfer system according to the third embodiment of the invention; [0071] Figure 21 is flow chart illustrating a method of time transfer for all embodiments; and [0072] Figure 22 shows a computing system, on which any of the above-described methods may be performed.

[0047] Common reference numerals are used throughout the figures to indicate similar features.

[0048] Detailed Description

[0049] Embodiments and arrangements of the present invention are described below by way of example only. These examples represent the best mode of putting the invention into practice that are currently known to the Applicant although they are not the only ways in which this could be achieved. The description sets forth the functions of the example and the sequence of steps for constructing and operating the example. However, the same or equivalent functions and sequences may be accomplished by different examples.

[0050] Some of the embodiments and arrangements below are described in relation to a quantum key distribution (QKD) system; however, such embodiments and arrangements described below are not limited to QKD systems. The embodiments and arrangements below can also, for example, be used in classical communication systems, or other systems, requiring time synchronisation and/or time transfer between two or more parts of a communication system, such as a satellite and a ground station. As described in further detail below, the two or more parts of the communication system can alternatively be a first ground station and a second ground station. Further, it will be understood that the embodiments and arrangements below can be used in any system requiring time transfer or synchronization between different clocks.

[0051] Some of the embodiments and arrangements below are described in relation to satellites and optical ground receivers (OGR). However, the invention is not limited to time synchronization and/or time transfer between satellites and optical ground receivers. The method and system of time synchronization and/or time transfer disclosed herein are applicable to any photon source and photon receiver arrangement comprising a plurality of clocks.

[0052] Figure 1 shows a schematic overview of a part of a satellite based quantum key distribution (QKD) system.

[0053] As shown in figure 1, satellite based quantum key distribution (QKD) system 1 comprises a satellite 2 and an optical ground receiver (OCR) 3 at a ground station. During a QKD session, the satellite 2 sends a quantum beam 4 comprising a series of single photons, or weak laser pulses attenuated such that each pulse contains a mean photon number of less than one, down to the OCR 3 with a particular repetition rate. Accordingly, in the illustrated example the satellite 2 acts a transmitter of the quantum beam 4, and the OCR 3 acts as a receiver of the quantum beam 4. In the illustrated example the quantum beam 4 comprises a series of laser pulses attenuated to the single-photon level. When the OCR 3 detects the laser pulses these detection events are time-stamped by the OCR 3. The OCR 3 and the satellite 2 then perform several post-processing steps. An example of one of these post-processing steps is basis reconciliation. In basis reconciliation, the basis choices for each detection event at the OCR 3 are compared to sending events at the satellite 2, and compatible detection events, that is, detection events which have compatible basis choices to sending events at the satellite 2, of single-photon laser pulses are retained and used as bases for subsequent encryption key negotiations, while detection events with incompatible bases are discarded. However, this requires the two parties to ensure they are comparing the same corresponding bits, such that every photon ID at the OCR matches the photon ID at the satellite. The photon IDs are the temporal labels for photon transmission and detection events.

[0054] For the satellite 2 and the OCR 3 to perform the required basis reconciliation and other post-processing steps to turn raw detection events into a secure key, the satellite 2 and the OCR 3 need to be very closely synchronised. This means that the satellite 2 and the OCR 3 must be able to match the sending event of a laser pulse at the satellite 2 to the detection event of the same laser pulse at the OCR 3. This is not a straightforward problem. In practice, because the laser pulses are single-photon events in order to provide the required quantum uncertainty, many sent photons are lost during transmission and never received by the OCR 3. Further, because the satellite 2 is in orbit, the satellite 2 is constantly moving relative to the OCR 3, so that the distance between the satellite 2 and the OCR 3 and the relative velocities of the satellite 2 and the OCR 3 are constantly changing. As a result, the link distance travelled by the quantum beam 4 between the satellite 2 and the OCR 3 is constantly changing, so that the time offset between the sending times at the satellite 2 and the reception times at the OCR 3 is constantly changing, and the repetition rate of the laser pulses received at the OCR 3 is also constantly changing due to Doppler shift. As a result, the synchronisation tolerances are very stringent. Hence a robust method for time-synchronisation is needed.

[0055] The present disclosure provides a means enabling the satellite and the OGR to synchronise their timings, so that their respective photon event identities can be synchronised and correlated. For example, so that they can perform the necessary QKD key post-processing steps on an aligned data set to allow them to share an identical secure key.

[0056] It will be understood that the satellite based QKD system 1 has many additional elements which are not shown in figure 1, and will not be described herein. It will also be understood that ills not essential for the satellite and OGR to be part a QKD system. The methods and systems of time synchronisation and time transfer can be implemented in other types of systems without QKD. Figure 1 is merely an explanatory diagram to assist in explaining the requirement for time synchronisation of the optical link between the satellite 2 and the OGR 3. Further, it will be understood that the QKD operation has numerous further steps in addition to basis reconciliation.

[0057] An overview of the present disclosure is for the satellite 2 to use a separate synchronisation laser operating at a wavelength well separated from the any other transmitted beams, such as the quantum beam 4. The synchronisation laser sends strong pulses at a lower repetition rate than the quantum beam, and having a pseudo random pattern. These pulses from the synchronisation laser are sent, along with the quantum beam 4, down to the OGR 3 where they are separated by their wavelength, for example by using a dichroic mirror.

[0058] The time synchronisation pulses sent by the synchronisation laser are detected by a dedicated detector, such as a photodiode. The OGR 3 matches its detections of the synchronisation pulses to its knowledge of the pseudo random pattern transmitted from the satellite 2 to establish the correct temporal starting point for the quantum beam 4. The OGR 3 may use a polynomial fit to establish the relationship between the actual system repetition rate and the assumed repetition rate, to synchronise the timing at the satellite 2 and the OGR 3. This established relationship can then be used to enable the photon detection events at the OGR 3 to be mapped to the photon transmission events at the satellite 2 (i.e. matching of photon IDs), such that the satellite 2 and the OGR 3 can perform the steps of key post-processing, such as error correction and privacy amplification, on the same transmitted and received bits.

[0059] Figure 2A shows a schematic diagram of a part of a time synchronisation system located on a satellite 2, while figure 2B shows a schematic diagram of a part of a time synchronisation system located at an OGR 3.

[0060] In figure 2A, the satellite 2 comprises an optical pulse generator 5, which produces a series of faint laser pulses at a first wavelength to form the quantum beam 4 at the first wavelength. The pulse generator 5 comprises a faint pulse laser system 6 controlled by pulse electronics 7. The faint pulse laser systems generates faint laser pulses at the first wavelength which are attenuated to single photon events, which faint laser pulses form the quantum beam 4 suitable for use in quantum key delivery (QKD) protocols. The pulse electronics 7 control the faint pulse laser system 6 to generate faint laser pulses allowing individual photons to be encoded for QKD protocols, such as prepare and measure QKD protocols. In the illustrated example, the emitted faint laser pulses are assigned photon IDs corresponding to the clock cycle of a shared clock 12 at which they are emitted. In the illustrated example the QKD system 1 operates using the BB84 polarisation encoding protocol, and the faint pulse laser system 6 comprises means to assign a polarisation state to each faint laser pulse. In some examples the faint pulse laser system 6 may contain a single photon source together with means to assign a polarisation state to each faint laser pulse.

[0061] The satellite 2 further comprises a synchronisation pulse generator 8, which produces a series of laser pulses at a second wavelength to form a synchronisation beam at the second wavelength. The synchronisation pulse generator 8 comprises a synchronisation laser 9 controlled by synchronisation electronics 10. The synchronisation laser 9 produces synchronisation pulses at the second wavelength to form the synchronisation beam 11. The first wavelength of the quantum beam 4 and the second wavelength of the synchronisation beam 11 are different wavelengths. The satellite 2 further comprises a shared clock 12, which provides common timing signals to both the pulse electronics 7 of the pulse generator band the synchronisation electronics 10 of the synchronisation pulse generator 8.

[0062] The quantum beam 4 and the synchronisation beam 11 are combined or multiplexed by a first dichroic mirror 12 of the satellite 2 into a single combined beam 13. The combined beam 13 is directed to the OGR 3 by output optics of the satellite 2 (not shown).

[0063] In figure 2B, the OGR 3 receives the combined beam 13 from the satellite 2 using input optics of the OGR 3 (not shown). The OGR 3 comprises a second dichroic mirror 14, which separates or demulitiplexes the received combined beam 13 into the quantum beam 4 and the synchronisation beam 11.

[0064] As discussed above, the first wavelength of the quantum beam 4 and the second wavelength of the synchronisation beam 11 are different wavelengths. The first and second wavelengths must be sufficiently different to allow robust separation or demultiplexing of the quantum beam 4 and the synchronisation beam 11 based on their wavelengths by the second dichroic mirror 14. However, the precise wavelengths used quantum beam 4 and the synchronisation beam 11 may be selected as appropriate in any specific implementation.

[0065] The OGR 3 comprises a decoding optical system 15 and a number of single photon detectors 16, which receive the quantum beam 4 and detect single photon reception events of the quantum beam 4. In the illustrated example of figure 2B, the decoding optical system 15 is arranged to decode according to the BB84 polarisation encoding protocol, and the decoding optical system 15 is a polarisation analyser. The OGR 3 further comprises a synchronisation pulse detector 17, which receives the synchronisation beam 11 and detects synchronisation pulse events of the synchronisation beam 11.

[0066] The respective outputs of the single photon detectors 16 and the synchronisation pulse detector 17 are provided to a time tagger 18, which time stamps the single photon reception events detected by the single photon detectors 16 and the received synchronisation pulse events detected by the synchronisation pulse detector 17 using a clock signal from a local clock 22 of the OGR 3.

[0067] The OGR 3 further comprises a timing recovery module 19, which analyses the timing of the received synchronisation pulse events based on their time stamps to carry out a time recovery operation and determine the timing difference, which may be referred to as the delta time (At), between the sending of the faint laser pulses by the satellite 2 and detection of the corresponding received single photons at the OGR 3, and adjusts or converts the timing of the single photon reception events as indicated by their respective time stamps accordingly, to enable correct matching of the sent faint laser pulses to the received single photons. The timing difference At is also referred to as a time of flight offset.

[0068] Figure 3 is an explanatory diagram illustrating some timing issues which may affect the QKD system 1 in operation [0093] As shown in figure 3, as the satellite 2 passes over the OGR 3 during a QKD communication session both the position and the velocity of the satellite 2 relative to the OGR 3 will continuously change throughout the communication session. As a result, for successive positions of the satellite 2 at successive times ti to t4, the respective path distance di to d4 of the quantum beam 4 between the satellite 2 and the OCR 3 may be different, and the respective rate of change of the path distance Ad, to Ad4 of the quantum beam 4 between the satellite 2 and the OCR 3 may also be different The path distance between the satellite 2 and the OCR 3 is temporarily static, and the rate of change of this path distance is temporarily zero, when the satellite 2 is at zenith. However, this is only the case for a very short period, and it is impractical for a satellite QKD system to function only in the short period when the satellite 2 is at zenith relative to the OGR 3. In practice, the system 1 must be able to operate in the more general case when the path distance and the rate of change of the path distance may be continually changing. As a result of these changes, the time required for the photons transmitted in the quantum beam 4 to travel from the satellite 2 will continuously change, and the rate of this change will also continuously change. This continually changing Doppler shift will result in a small, but continuous, change in the effective pulse repetition rate of the faint laser pulses received at the OCR 3, compared to the actual pulse repetition rate of these pulses transmitted by the satellite 2. Although this is a small change, the cumulative effect would, if not corrected, cause synchronisation between the satellite 2 and the OCR 3 to quickly fail, typically in less than second. As a result, it may be difficult to correlate which photon detection events at the OCR 3 correspond to which photon transmission events at the satellite 2, making QKD protocols, which depend upon such correlation, unreliable. In addition to the timing changes resulting from the relative movement of the satellite 2 and OCR 3, there may also be unpredictable random short time scale errors in pulse generation, pulse detection, and time tagging, generally referred to as timing jitter. In the illustrated example, the first wavelength is 850 nm. This is not essential, and other wavelengths may be used in alternative examples.

[0069] Figure 4A shows a schematic diagram showing laser pulse sequences of the quantum beam 4 and the synchronisation beam 11 generated on board the satellite 2.

[0070] As shown in figure 4A, the faint pulse laser system 6 generates faint laser pulses 20 at the first wavelength which are attenuated to single photon events, which faint laser pulses 20 form the quantum beam 4 suitable for use in QKD protocols, in the illustrated example, the BB84 protocol. In the illustrated example, the faint pulse laser system 6 emits pulses 20 at a frequency of around 2 GHz, so that the pulses are separated by around 500 ps. Accordingly, the errors and/or uncertainty in the relative timings of pulse emission at the satellite 2 and pulse reception at the OCR 3 should be in the order of hundreds of picoseconds or less in order for the emitted and received photons to be correctly and unambiguously correlated.

[0071] The synchronisation laser 9 generates synchronisation laser pulses 21 at a second wavelength which form the synchronisation beam 11. The emission of the synchronisation laser pulses 21 and the faint laser pulses 20 are synchronised by the satellite 2, and any fixed timing offset between them is determined and provided to the OGR 3, for example, in advance of the QKD communication session. This offset for the satellite 2 may be distributed to all OGRs 3 in the QKD system 1 by a system controller of the QKD system 1. As discussed above, the quantum beam 4 and the synchronisation beam 11 are combined by the first dichroic mirror 12 into a single combined beam 13, which is transmitted to the OGR 3. In the illustrated example, the second wavelength is 1525 nm. This is not essential, and other wavelengths may be used in alternative examples.

[0072] The synchronisation laser pulses 21 are emitted with a predetermined data baud rate, or repetition rate, in a pseudo random pattern having a predetermined length and frame rate.

[0073] The baud rate is the symbol rate of the synchronisation beam 11 signal, which may be regarded as the repetition frequency of synchronisation laser 9, assuming that a pulse 21 were sent in every time interval, although for the time correlation procedure, some pulses are blocked to allow 'Os' to be sent as well as as symbols to form the pseudo random pattern.

[0074] In the illustrated example, the baud rate or repetition rate is around 1 kHz, so that the pulse positions are separated by about 1 ms, and the pseudo random pattern has a length of 3 seconds, and thus a frame rate of about 0.33 Hz. The pseudo random pattern comprises digital ones and zeros represented by the presence and absence of a pulse 21 at each pulse position. It should be noted that the illustrated time separations between the faint laser pulses 20 and the synchronisation laser pulses 21 are not shown to scale in the figures.

[0075] The pseudo random pattern used at the satellite 2 is known to the OGR 3 in advance.

[0076] Conveniently, the satellite 2 can always use the same pseudo random pattern, and all satellites 2 in a QKD system 1 can use the same pseudo random pattern, so that the OGRs 3 of the system 1 only need to know a single, fixed, pseudo random pattern. However, in principle, the pseudo random pattern used can change over time and/or be different for different satellites, provided that this is known to the OGR 3. In the illustrated arrangement, the pseudo random pattern is a de Bruijn sequence with a length of 3 seconds. This is not essential, and other patterns and/or lengths of the synchronisation laser pulses 21 may be used in alternative examples [0099] Using a pseudo-random pattern rather than an alternating sequence of ones and zeros makes the procedure significantly more robust to missed pulses. A useful way of defining the sequence is to use de Bruijn sequences, which are strings which contain all possible substrings of a particular length exactly once. For example, assuming an alphabet of size n =2 (corresponding to 0 and 1) and a substring length of k=3, the de Bruijn sequence would be as follows: 0 0 0 1 0 1 1 1. In general, the length of the de Bruijn sequence is Ilk.

[0077] [00100]The pattern used for the synchronisation pulses should be pseudo random, non-repeating and ideally balanced, having an equal number of 1s and Os, so that the OGR3 cannot inadvertently lock onto the wrong part of the pattern. However, the use of a de Bruijn sequence may provide improved resilience to mismatching or signal noise.

[0078] [00101] Figure 49 shows a schematic diagram showing laser pulse sequences of the quantum beam 4 and the synchronisation beam 11 received at the OCR 3.

[0079] [00102] The OCR 3 receives the combined beam 13 from the satellite 2, and the combined beam 13 is separated by the second dichroic mirror 14 into the quantum beam 4 and the synchronisation beam 11. The faint laser pulses 20 of the quantum beam 4 then go to the decoding optical system 15 (the polarisation analyser) and single photon detectors 16, and the synchronisation pulses 21 of the synchronisation beam 11 go to the synchronisation pulse detector 17. Both faint laser pulse 20 and synchronisation pulse 21 detection events are time-stamped with reference to the same OCR local clock by the time tagger 18.

[0080] [00103]Th The timing recovery module 19 carries out a time correlation process to determine a time correction which can be used to transform or convert the timings of the single photon reception events detected by the single photon detectors 16 at the OCR 3 to the timings of the corresponding faint laser pulse emissions at the satellite 2, and so synchronise these timings. It will be understood that this time correction is not a fixed value, but varies over time, because the path distance of the quantum beam 4 between the satellite 2 and the OCR 3 varies over time, and the effective repetition rate of the received pulses is changing due to Doppler shift as a result of relative movement of the satellite 2 with respect to the OCR 3 The time correction can also be referred to as a time of flight offset.

[0081] [00104] Figure 5 shows a flow chart of a time correlation process 50 carried out by the OCR 3 according to the first arrangement. Although the satellite 2 generates the pulses 20 and 21 of the quantum beam 4 and the synchronisation beam 11, the satellite 2 does not carry out the time correlation process 50, which is carried out entirely at the OCR 3.

[0082] [00105]Th The start time for a QKD session between the satellite 2 and the OCR 3 is scheduled in advance. Generally, such scheduling is carried out in advance for the QKD system 1 as a whole by a central control station, and an agreed start time for the establishment of a quantum communications link between the satellite 2 and the OCR 3 is set and communicated to the satellite 2 and the OCR 3. At the agreed quantum link start time, the satellite 2 generates the first synchronisation pulse 21 and the first faint laser pulse 20 simultaneously, using the synchronisation laser 9 and the faint pulse laser system 6.

[0083] [00106]The time correlation process 50 begins when the first synchronisation pulse 21 of the QKD session is detected by the synchronisation pulse detector 17 of the OGR 3 in a quantum link start block 51. It should be understood that it is possible that the first synchronisation pulse 21 which is detected may not be the first synchronisation pulse 21 which was transmitted, because ills possible that the first one or more synchronisation pulses 21 may have been lost, that is, transmitted but not received.

[0084] [00107] Received synchronisation pulses 21 detected by the synchronisation pulse detector 17 are time-tagged, or time stamped, with the time of receipt according to a clock of the OGR 3 by the time tagger 18, and provided to the timing recover module 19, in a gather synchronisation pulses block 52.

[0085] [00108]The gathered synchronisation pulses are then analysed by the timing recovery module 19 in a time slope estimation block 53. The timing recovery module 19 analyses the time separation of the detected synchronisation pulses and uses this to estimate the relative time slope, or clock slope, that is, the difference between the measured repetition rate (baud rate) of the synchronisation pulses received at the OGR 3 according to the clock of the OGR 3 and the known repetition rate (baud rate) of the synchronisation pulses sent by the satellite 2 according to the clock 12 of the satellite 2. This clock slope difference will comprise both differences in the actual clock rates of the clocks used by the satellite 2 and the OGR 3, and also changes between the sent and received pulse timings due to Doppler effects. Doppler effects in this case are the shift in the measured repetition rate that results due to motion of the satellite 2 towards or away from the OGR 3 as it carries out a pass, which changes the path length between the satellite 2 and the OGR 3, and so changes the travel time of the synchronisation pulses 21 and the faint laser pulses 20 between the satellite 2 and the OGR 3. At zenith, the distance between the satellite 2 and OGR 3 is fixed, and hence there is no Doppler shift at this time.

[0086] [00109] The timing recovery module 19 identifies the first pulse detected by the synchronisation pulse detector 17 as the first pulse in the frame. The timing recovery module 19 then determines an expected last pulse time which is one transmitted frame time (the known time taken to transmit the full pseudo random pattern at the satellite 2) later than the time at which the first pulse was received. The timing recovery module 19 then identifies the detected pulse with a reception time closest to the expected last pulse time as the last pulse in the frame. The following pulse is then identified as the first pulse of the next frame, and the process is repeated to identify the last pulse of the next frame, and so on.

[0087] [00110]This simple manner of identifying the first and last pulses of each transmitted pseudo random pattern assumes that the clock slope errors are relatively small, so that the accumulated error over a full frame of the pseudo random pattern is less than half the time between successive synchronisation pulses, so that it is easy to identify the last pulse of a pseudo random pattern frame based on timing. In the illustrated example where the transmitted frame time is 3 seconds and the pulse rate or baud rate is 1 kHz, this requires an accumulated error of less than 0.5 ms after 3 seconds. A difference in clock rate at the satellite 2 and OGR 3 of about 1 second per day would have an error of 0.034 ms after 3 seconds, and clocks having this level of error are readily available. Further, Doppler effects are expected to be relatively small, because satellite orbital velocities are small compared to the speed of light. For example, for a clock rate of 2GHz at the satellite 2 and the OGR 3 it is expected that a worst case change in received clock rate would be no more than about +/-50 kHz. Accordingly, it is expected that it will be straightforward in practice to select clock sources and baud and frame rates which allow this simple approach to be used.

[0088] [00111]When a full frame of the pseudo random pattern has been received, the timing recovery module 19 identifies the first and last pulses in the frame, that is, the first and last pulses of the full frame of the pseudo random pattern, as discussed above, and compares the timings of the first and last pulses using their time stamps to determine the time difference between them. As is discussed above, the OGR 3 knows the baud rate and the frame rate of the pseudo random pattern sent by the satellite 2. Accordingly, the timing recovery module can determine the clock slope difference by comparing the measured time taken to receive the full pseudo random pattern at the OGR 3, the received frame time, to the known time taken to transmit the full pseudo random pattern at the satellite 2, the transmitted frame time, and determining the time difference between the measured receiving time and the known transmitted time. The timing recovery module 19 then divides the number of symbols in a complete frame of the pseudo random pattern by the determined time difference to calculate the clock slope in terms of a frequency difference between the baud rate of the transmitted pseudo random pattern at the satellite 2, which is based on the clock rate of the shared clock 12 of the satellite 2, and the apparent baud rate of the pseudo random pattern received at the OGR 3 according to the local clock 22 of the OGR 3. The clock frequencies of the shared clock 12 and the local clock 22 are intended to be the same, so this determined clock slope frequency difference will comprise frequency differences in the transmitted and received baud rates due to any difference in the actual clock frequencies of the shared clock 12 and the local clock 22 together with effects due to the relative movement of the satellite 2 and the OGR 3. It will be understood that, as explained above, the first synchronisation pulse detected is not necessarily the first synchronisation pulse sent, and so may not be the actual first pulse in a frame of the pseudo random pattern. However, since the synchronisation laser pulses 21 are emitted with a predetermined data baud rate this will not affect the calculation of the clock slope.

[0089] [00112] Determining the clock slope across a full frame length of the pseudo random pattern comprising multiple pulses reduces the effect of timing errors (jitter) associated with individual pulses, and may allow a more accurate determination of the clock slope. The jitter associated with individual pulses is made up of short time scale errors in the pulse generation, pulse detection, and time tagger systems for both the faint pulse laser pulses 20 and the synchronisation laser pulses 21. This jitter is noise which needs to be filtered out by the time correlation process 50, and this filtering out is assisted by determining the clock slope across a full frame of the pseudo random pattern.

[0090] [00113] When a full frame of the pseudo random pattern has been received, and the clock slope for this received frame has been calculated, the timing recovery module 19 uses the calculated clock slope to carry out an initial adjustment of the timings of the received synchronisation pulses 21 in a slope correction block 54. This initial adjustment alters the relative timings of the received synchronisation pulses 21 of the received frame to correct for the calculated clock slope, so that the relative timings of the received synchronisation pulses 21 more accurately correspond to the known relative timings of the transmitted synchronisation pulses 21. In some examples this initial adjustment may be carried out by keeping the timing of the first pulse of the received frame fixed, and altering the relative timings of subsequent pulses based on the calculated clock slope. However, in other examples a different adjustment technique may be used.

[0091] [00114] Following the initial adjustment in the slope correction block 54, the timing recovery module 19 correlates the received synchronisation pulses to the known pulses of the pseudo random pattern in a match pulse patterns block 55 [00115] Figure 6 is an explanatory diagram showing the correlation process carried out in the match pulse patterns block 55. The timing recovery module 19 correlates the adjusted synchronisation pulses 60, that is, the received synchronisation pulses 21 after the initial timing adjustment based on the calculated clock slope, to the known pulses 61a of the pseudo random pattern bit-by-bit, and determines the correlation coefficient CCo for the correlation. A correlation coefficient indicates the quality of matching between two patterns, in this case the percentage of matched values between the known and detected pulse sequences.

[0092] [00116] The timing recovery module 19 then repeats the correlation process and correlates the received synchronisation pulses to the known pulses 61b of the pseudo random pattern shifted by one pulse (one bit), and determines a correlation coefficient CCi for the correlation.

[0093] This is repeated for the full number of pulses in the pseudo random pattern, so that a correlation coefficient is determined for every possible relationship between the received and transmitted pulse patterns.

[0094] [00117] The timing recovery module then compares the determined correlation coefficients and identifies the relative position having the highest correlation coefficient as the correct relative position of the adjusted synchronisation pulses to the transmitted pseudo random pulse pattern, and so identifies the relationship of the local clock time at the OGR 3 to the clock time at the satellite 2. Comparing the correlation at different positions in this way allows the correct relative time positions of the received and transmitted pulse patterns to be determined even when some of the received pulses may be incorrect. In any received pseudo random pattern frame some transmitted pulses may not be received, for example due to clouds, so that transmitted ones are incorrectly received as zeros. In principle, some transmitted zeros could be incorrectly received as ones, but this is less likely.

[0095] [00118] When the correct relative position of the corrected synchronisation pulses to the transmitted pseudo random pulse pattern has been identified, the first received synchronisation pulse can be matched to the corresponding transmitted synchronisation pulse, and to the quantum link start time, so that the time when the first received pulse was transmitted by the satellite 2 and received by the OGR 3 can be matched as to, so that the satellite 2 and the OGR Scan have the same knowledge of the timing of the first photon transmitted through the quantum beam, and they are agreed which photon ID is photon ID = 1, the first photon transmitted through the quantum beam at the start of the QKD session.

[0096] [00119] Then, the timing recovery module 19 calculates a synchronising conversion of OGR time according to the clock of the OGR 3 to satellite time according to the clock 12 of the satellite 2 in a curve fitting block 56. The timing recovery module 19 carries out the curve fitting by taking the matched relative positions of the adjusted received synchronisation pulses and the sent pseudo random pulse pattern identified in the match pulse patterns block 55, and fitting a function, such as a polynomial function, to the relationship between the OGR time (the time according to the local clock 22) indicated by the adjusted received synchronisation pulse times and the satellite time (the time according to the shared clock 12) indicated by the transmitted synchronisation pulse times over a short period of time, for example 1 second.

[0097] The determined function, such as a polynomial function, defines the relationship between the emission times at the satellite 2 and the actual detection times at the OGR 3. The pulse travel time between the satellite 2 and the OGR 3 is constantly changing, so that the relationship between the emission times and the detection times is also constantly changing, so that the use of a polynomial function for the fitting may provide greater accuracy than a linear fit.

[0098] However, the use of a polynomial function is not essential, and in other examples a different function may be used. In some other examples, a regression analysis technique, such as segmented linear regression, or spline fitting, may be used instead of polynomial function fitting. In some other examples, a model of the underlying physical system could be used, and the parameters of the system tuned to fit the data, instead of polynomial function fitting.

[0099] [00120] Then, the timing recovery module 19 uses the polynomial, or other, function determined in the curve fitting block 56 to convert or translate the single photon reception times to faint pulse laser system pulse emission times in a time translation block 57. As discussed above, the synchronisation pulses have been used to retrieve the relationship between the satellite 2 time and the OGR 3 time, this relationship being defined by the determined polynomial, or other, function. The timing recovery module 19 uses the polynomial, or other, function to translate the reception times of the received single photons of the quantum beam 4 according to the OGR 3 clock, as indicated by the associated time stamps, into the corresponding transmission or sending times at the satellite 2 according to the satellite clock, and so synchronise the timing of the reception times and the sending times.

[0100] [00121] The timing recovery module 19 then translates the determined synchronised transmission times into photon IDs in a determine photon ID block 58. In the illustrated example the photon IDs are not directly based on the determined transmission times. Instead, the translated reception times, which have been translated into sending times at the satellite 2 according to the satellite clock, are converted to photon IDs by taking the nearest cycle time of the shared clock 12 of the satellite to the determined transmission times. This translation to photon IDs is possible because the synchronisation laser 9 and faint pulse source laser 6 are driven by the same master clock 12 on-board the satellite 2.

[0101] [00122] The received photon events can then be matched with photon emission events using their respective photon IDs and the satellite 2 and the OGR 3 can use the matched events to perform QKD key post-processing steps in a conventional manner so that they can negotiate and share an identical secure key or keys.

[0102] [00123] The use of a correlation process in combination with the polynomial fitting provides a method of time translation which is robust to noise and missed pulses, and minimises the probability of incorrect correlation.

[0103] [00124] The procedure described above may allow sufficiently accurate time synchronisation/translation to support quantum beam pulse repetition rates greater than 1 GHz, with timing errors being reduced to the order of hundreds of picoseconds, compared to previous satellite QKD systems, which typically can support repetition rates of only up to around 100 MHz because of the large timing synchronisation errors. Further, through the use of a pseudo random pulse pattern the pseudo random nature of the pulses may provide greater robustness to noise in the communication channel, which can obscure detection events, and greater robustness to noise introduced in the pulse generation and detection processes. The present approach does not require additional channels or communication between satellite and ground station (OGR). All correlation is performed on the ground at the OGR after reception and detection of time synchronisation pulses from the satellite.

[0104] [00125] In the illustrated first arrangement the photon ID used is based on the satellite 2 clock cycles. In other examples where a different photon ID is used, the photon ID block 57 may be changed to a different manner of translating the determined times into photon IDs may be used as appropriate. In examples where the transmission or reception time is used directly as the photon ID, the photon ID block may be omitted.

[0105] [00126] In the illustrated first arrangement the method used to identify the last pulse in each frame of the transmitted pseudo random pattern assumes a relatively small difference in clock rate. In examples where the difference in clock rate may be larger, an alternative method may be used to do this. In some examples this may be done by comparing the times of the received pulses to determine an approximate value of the time difference between received bits (ones or zeros). It will be understood that the time period between successive received pulses (ones) will always be an integer multiple of this value. This value and the known bit length of the pseudo random pattern can then be used to identify the last pulse in the frame.

[0106] [00127] In the illustrated first arrangement the photon reception times at the OGR 3 according to the OGR clock are translated into photon emission times at the satellite 2 according to the satellite clock. This may provide the advantage of minimising communication between the OGR 3 and the satellite 2, and minimising the amount of computation which must be carried out on the satellite. However, this is not essential, and in principle, the same techniques could be used to translate the photon emission times according to the satellite clock into photon reception times according to the OGR clock. In other examples, the OGR 3 could send the synchronisation pulse detection time information, such as timestamps, to the satellite 2, and the satellite 2 could carry out the time adjustment calculations to allow the received photon events to be matched with corresponding photon emission events.

[0107] [00128] In practice, it is expected that a time offset will exist between the reception times of the faint pulse source pulses and the synchronisation pulses at the OGR 3 even when the emission of the different pulses is triggered simultaneously, for example by the same clock pulse of the shared clock 12. This may, for example, be due to path length differences on board the satellite, and may also be the result of the different wavelengths of the faint pulse source pulses and the synchronisation pulses causing a variation in travel time through the atmosphere even though the path length through the atmosphere is the same for the different pulses at any given time. Further, in a system using polarisation encoding there may be different time offsets for each polarisation state Where the BB84 protocol is used there may be four different time offsets for the four different polarisation states of the faint pulse source pulses/single photons.

[0108] [00129] This fixed time offset will interfere with post processing in a similar manner to any variable time errors, and in general it is desirable that both the fixed offset and the dynamic timing error will need to be corrected. The dynamic timing errors are corrected for each QKD communication session between the satellite 2 and OGR 3 during the communication session, as described above. Optionally, any fixed timing offset can be measured in a dedicated calibration or housekeeping session scheduled between the satellite 2 and the OGR 3. In some examples the time offset(s) may be slowly varying, for example due to thermal or aging effects on system components. In such examples where slowly varying time offsets are expected, the dedicated calibration or housekeeping session may be repeated at intervals to account for these variations. In this context, a slowly varying time offset is one which will not change significantly during a communication session.

[0109] [00130] In a system using polarisation encoding, such as the illustrated system using the BB84 protocol, the OGR 3 could generate a histogram of photon detection events at each polarisation detector, and analyse the histogram to estimate the timing offsets of the different polarisation channels from one another. This may be done in operation of the system 1 without the need for a dedicated calibration or housekeeping session. However, it is expected that the use of a dedicated calibration or housekeeping session will allow more accurate determination of the fixed time offsets.

[0110] [00131] In some examples, the offset, or offsets, can be systematically scanned by the satellite 2 in a dedicated housekeeping/calibration mode during which the OGR 3 requests the satellite 2 to send faint pulses having specific states, such as polarisation values, and calculates the quantum bit error rate (QBER) for each state, which in this scenario can be thought of as an indication of the amount of misregistered photons, at different time offset values. At the optimum time offset, where the time offset value corresponds to the actual fixed timing offset, the lowest QBER would be observed. This optimum timing offset can then be used for that state for all subsequent contacts. Further, the optimum timing offset can also be sent to other OGRs 3 to minimise the amount of time that the OGRs 3 and the satellite 2 spend in the housekeeping/calibration mode. In some examples, the determined timing offsets can be sent to a control centre of the satellite QKD system 1 for distribution to other OGRs 3.

[0111] [00132] In alternative examples, the satellite 2 can send a known sequence of polarisation states in the quantum beam 4 to the OGR 3, such that the time offset could be retrieved through post processing at the OGR 3. An explanatory example of this example is shown in figure 7.

[0112] [00133] As shown in figure 7, during a dedicated housekeeping/calibration mode, the satellite 2 emits a known pattern of faint laser pulses 20. This known pattern can conveniently be a stream of predetermined length of each possible polarisation state. The OGR 3 receiving the faint laser pulses 20 would then detect the faint laser pulses and determine the timing offset between each of them and the synchronisation pulses. The determining of the timing offset between each of the faint laser pulses and the synchronisation pulses employs the techniques described above for time slope determination and correction, and matching and fitting of the pseudo random code patterns, and also for the known patterns of faint laser pulses, in order to minimise the impact of satellite movement related delay and Doppler effects, and timing jitter, on the determined timing offset. The determined timing offset for each state can then be used for that state for all subsequent contacts. Further, the determined timing offset for each state can be distributed to other OGRs 3 to minimise the amount of time that the OGRs 3 and the satellite 2 spend in the housekeeping/calibration mode. In some examples, the determined timing offsets can be sent to a control centre of the satellite QKD system 1 for distribution to other OGRs 3.

[0113] [00134] The first arrangement is described as using the BB84 protocol. In other examples, alternative protocols may be used. In some examples, the BBM92 photon entanglement protocol may be used.

[0114] [00135] Figure 8 shows a schematic diagram of a part of a time synchronisation system 80 according to a second arrangement The time synchronisation system 80 is located on a satellite 2 and an OGR 3.

[0115] [00136] As shown in figure 8, the satellite 2 comprises a pulse generator 82 comprising a faint pulse laser system, which produces a series of faint laser pulses to form a quantum beam 81.

[0116] The pulse generator 82 generates faint laser pulses which are attenuated to single photon events, which faint laser pulses form the quantum beam 81 suitable for use in quantum key delivery (QKD) protocols. In the illustrated example, the emitted faint laser pulses are assigned photon IDs corresponding to the clock cycle of a clock 83 at which they are emitted.

[0117] In the illustrated example the QKD system 1 operates using the BB84 polarisation encoding protocol. In some examples the faint laser pulses may be produced by a single photon source.

[0118] [00137] The quantum beam 81 is directed to the OGR 3 by output optics of the satellite 2 (not shown).

[0119] [00138] The OGR 3 receives the quantum beam 81 from the satellite 2 using input optics of the OGR 3 (not shown). The OGR 3 comprises a decoding optical system 84 and a number of single photon detectors 85, which receive the quantum beam 81 and detect single photon reception events of the quantum beam 81, and the respective properties of the received photons. In the illustrated example of figure 8, the decoding optical system 84 is arranged to decode according to the B984 polarisation encoding protocol, and the decoding optical system 84 is a polarisation analyser. The output of the single photon detector 85 is provided to a time tagger 86, which time stamps the single photon reception events detected by the single photon detector 85 using a clock signal from an OGR 3 local clock 88. The OGR 3 further comprises a timing recovery module 87.

[0120] [00139] In the second arrangement, there is no separate synchronisation pulse laser, as used in the first arrangement. Instead, at predetermined times during the communication session between the satellite 2 and the OGR 3, the faint pulse laser system is not used to generate single photons randomly encoded in polarization as a quantum beam for QKD generation. That is, the faint pulse laser system itself is instead used to create a series of synchronization pulses at regular time intervals which are encoded with a pseudo random code, that are used to support the OGR time correlation procedure discussed above with reference to the first arrangement.

[0121] [00140] In some examples, the predetermined times when the faint pulse laser system is used to create synchronization pulses may be distributed at regular time intervals during the sending of the faint laser pulses 20 forming the quantum beam by the faint pulse laser system. For example, the faint pulse laser system may be used to create a synchronization pulse in place of every n-th faint laser pulse, where n is an integer greater than 1, such as n=100. In other examples, the predetermined times when the faint pulse laser system is used to create synchronization pulses may be distributed at regular time intervals during a dedicated calibration time period when the faint pulse laser system does not send faint laser pulses 20. In order to do this, the pulse generator 82 is arranged to encode the series of predetermined ones of the faint laser pulses in a manner different from the encoding of the remaining faint laser pulses, which remaining faint laser pulses form a series of faint laser pulses which provide the quantum beam.

[0122] [00141] In the second arrangement, in some examples, this encoding is carried out by allowing photons to be transmitted at a higher intensity, for example without the faint laser pulse source being attenuated down to the single photons level required for quantum transmission, to generate a more intense synchronisation pulse. The single photon detector(s) 85 of the OGR 3 can then be used to detect the synchronisation pulses.

[0123] [00142] In some examples where a polarisation encoding protocol is used, this encoding may be achieved by allowing photons to be transmitted in all polarization channels, and possibly also at a higher intensity, such as without the source being attenuated down to the single photons level required for quantum transmission, to generate a more intense synchronisation pulse. The single photon detector(s) 85 of the OGR 3 can then be used to detect these synchronisation pulses.

[0124] [00143] Although only a predetermined part of the faint laser pulses are used to form the series of time synchronisation pulses (for example using every 100th pulse), due to the much higher pulse repetition rate of the faint laser pulses than the dedicated synchronisation pulses in the first arrangement, the number and rate of time synchronisation pulses received and available at the OGR 3 receiver in the second arrangement may be substantially equal to, or greater than, in the first arrangement. It is expected that, in the example of faint pulses being emitted ever 500 ps, using every 100th faint pulse as a time synchronisation pulse will provide detection rates for synchronisation pulses at a similar frequency to the first arrangement.

[0125] Although the individual time synchronisation pulses will be weaker because they come from a weaker source, and so will be more difficult to detect, leading to a lower detection probability, their greater rate will allow a similar process to be used to analyse and use the time synchronisation pulses to correct or translate the faint pulse reception times at the OGR 3 to faint pulse transmission times at the satellite 2, or vice-versa [00144] The sent and received synchronisation pulses can then be processed by the timing recovery module 87 to determine and adjust for clock slope, and to determine a function, such as a polynomial function, in a similar manner to the first arrangement. This function can then be used to translate the reception times of the received single photons of the quantum beam 81 according to the OGR 3 clock 88, as indicated by the associated time stamps, into the corresponding transmission or sending times at the satellite 2 according to the satellite clock.

[0126] [00145] The second arrangement may allow the requirement for dedicated equipment to generate and receive the synchronization laser pulses to be eliminated on both the satellite and the OGR. Further, this may simplify optical design of the satellite and reduce the impact of atmospheric divergence between the synchronisation and quantum laser downlinks.

[0127] However this approach may not be compatible with some protocols, such as the BBM92 or E91 entanglement based protocols. Further, this approach may present difficulties for BB84, or other prepare and measure protocols due to the strenuous requirements this places on the FPS between its maximally on and maximally off states.

[0128] [00146] A time synchronisation method according to a third arrangement may also be carried out using the synchronisation system 80 illustrated in figure 8.

[0129] [00147] According to the third arrangement, the synchronisation system 80 is located on a satellite 2 and an OGR 3 comprising corresponding components to those described above with reference to the second arrangement Similarly to the second arrangement, the satellite 2 generates a quantum beam 81 comprising a series of faint laser pulses, and this quantum beam 81 is received, and single photon reception events of the quantum beam 81 detected, together with the respective properties of the received photons, by the OGR 3 [00148] In the third arrangement, similarly to the second arrangement, there is no separate synchronisation pulse laser, as used in the first arrangement. Instead, in the third arrangement, during the communication session between the satellite 2 and the OGR 3, the system 80 is arranged to use a series of predetermined ones of the faint laser pulses as a series of time synchronisation pulses.

[0130] [00149] In order to do this, the pulse generator 82 is arranged to encode the series of predetermined ones of the faint laser pulses in a predetermined manner. In some examples, this encoding may comprise encoding the predetermined ones of the faint laser pulses with a significant bias between different states compared to the relationship between the different encoding states for the remaining faint laser pulses. In examples encoded using different polarisation states where the faint laser pulses are encoded with a plurality of different polarisation states, the predetermined ones of the faint laser pulses may be encoded with only a sub-set of these different polarisation states, and with a different bias between the states of this sub-set compared to the remaining faint laser pulses. For example, the system 80 may be arranged to use each 100th faint laser pulse as a time synchronisation pulse, so that the series of 100th faint laser pulses form a series of time synchronisation pulses. In some examples using the BB84 polarisation encoded protocol, the pulse generator 105 may be arranged to encode each 100th faint laser pulse in the horizontal/vertical (HN) basis only, with a significant bias between the two states, for example 90% V and 10% H. The pattern of the H and V encodings in this series of faint laser pulses would then provide a predetermined known pseudo random pattern, as discussed with reference to the first arrangement. The single photon detector(s) 85 of the OGR 3 can then be used to detect the synchronisation pulses and their polarisation states [00150] For example, the system 80 may be arranged to use each 100th faint laser pulse as a time synchronisation pulse, so that the series of 1001h faint laser pulses form a series of time synchronisation pulses. In some examples, the pulse generator 82 may be arranged to encode each 100th faint laser pulse in the horizontal/vertical (H/V) basis only, with a significant bias between the two states, for example 90% V and 10% H. The pattern of the H and V encodings would be a predetermined known pseudo random pattern, as discussed with reference to the first arrangement.

[0131] [00151] Although only a predetermined part of the faint laser pulses are used to form the series of time synchronisation pulses (in the example using every 100th pulse, 1 percent of the faint laser pulses are used as the series of time synchronisation pulses), due to the much higher pulse repetition rate of the faint laser pulses than the dedicated synchronisation pulses in the first arrangement, the number and rate of time synchronisation pulses available at the OGR 3 receiver in the third arrangement may be greater than in the first arrangement. It is expected that, in the example of faint pulses being emitted ever 500 ps, using every 100th faint pulse as a time synchronisation pulse will provide detection rates for synchronisation pulses at a similar frequency to the first arrangement. Although the individual time synchronisation pulses will be weaker because they come from a weaker source, and so will be more difficult to detect, leading to a lower detection probability, their greater rate will allow a similar process to be used to analyse and use the time synchronisation pulses to correct or translate the faint pulse reception times at the OGR 3 to faint pulse transmission times at the satellite 2, or vice-versa.

[0132] [00152] In the third arrangement, the same principles may be used to carry out the time correction/translation, although the processing of the received time synchronisation pulses will generally be more complex. For example, in the third arrangement a fast-fourier transform (FFT) may be used on the faint pulse detection events to extract an estimate of the system repetition rate (that is, the faint pulse detection rate at the OGR 3), and this could be used to determine the time slope, as an alternative to determining the time slope from the series of time synchronisation pulses only. However, the method of obtaining the pseudo-random pattern and using this to obtain a function translating or correcting the faint pulse reception times at the OGR 3 to faint pulse transmission times at the satellite 2, or vice-versa, would be the same.

[0133] [00153] The third arrangement may allow the requirement for dedicated equipment to generate and receive the synchronization laser pulses to be eliminated on both the satellite and the OGR. Further, this may simplify optical design of the satellite and reduce the impact of atmospheric divergence between the synchronisation and quantum laser downlinks. However this approach may impose key rate overhead, and may introduce additional encoding and quantum downlink decoding complexity. Further, without wishing to be bound by theory, it is expected that this approach may be more sensitive to errors and attenuations introduced in the link due to the decreased power of the quantum beam compared to a dedicated synchronisation beam.

[0134] [00154] The embodiments and arrangements described herein have a quantum downlink beam from a satellite to a ground station, with various components located on the satellite or at the ground station. In alternative examples, this arrangement may be reversed, and the SQKD system may comprise a quantum uplink beam from a ground station to satekte, with the locations of the various system components being reversed. Other arrangements are also possible, where the quantum beam is between two satellites or two ground stations, with the various system components being arranged appropriately at the transmission and reception ends of the quantum beam.

[0135] [00155] In the embodiments and arrangements described herein, a single quantum beam between a satellite and a ground station is shown. In some examples, such as systems using entanglement based protocols, such as the BBM92 protocol, there may be two quantum beams used simultaneously between a satellite and two different ground stations, wth each quantum beam being directed by a separate dedicated optical terminal on the satellite. In such examples, time synchronisation of each of the quantum beams may be independently adjusted by the methods described herein. In systems using entanglement based protocols, such as BBM92, where the faint pulse source is used to produce the synchronisation pulses, it will be necessary to provide both a faint pulse source and an entanglement source at the transmitter (the satellite in the illustrated embodiments and arrangements). In systems using entanglement based protocols, such as BBM92, it will be necessary to have either the same synchronisation laser or faint pulse source laser being split into both downlink optical chains forming a quantum beam, or if a separate synchronisation laser or faint pulse source laser is used for each downlink optical chain forming a quantum beam, these lasers must be synchronised to a common clock, or have any timing offset calibrated out.

[0136] [00156] In the embodiments and arrangements described herein the faint pulses are single photon events. In other examples, these may be multi-photon events. The multi-photon events can be a series of entangled photons.

[0137] [00157] In the embodiments and arrangements described herein the system comprises a single optical ground receiver (OGR). The system may comprise any number of OGRs. In a multi-photon event, where the photons are entangled, the plurality of OGRs can be synchronised with the satellite.

[0138] [00158] In the embodiments and arrangements described herein the system comprises a single satellite. The system may comprise any number of satellites.

[0139] [00159] In the embodiments and arrangements described herein, each of the satellite and the OGR includes a single dichroic mirror to combine and separate the different optical beams. In other examples, different beam combining or separating arrangements may be used.

[0140] [00160] In the embodiments and arrangements described herein, a polynomial fit is used. In other examples, different types of fit may be used.

[0141] [00161] In the embodiments and arrangements described herein, specific laser wavelengths and pulse repetition rates are used. In other examples, different wavelengths and/or pulse repetition rates may be used.

[0142] [00162] In the embodiments and examples described herein, a faint pulse source (FPS) is used to generate the pulses of the quantum beam. In other examples, alternative sources for these pulse may be used, such as true single photon sources, or entanglement pair sources (for use in entanglement protocols such as BB92 or E91). These examples of alternative sources are not exhaustive.

[0143] [00163] Figure 9 is a schematic diagram illustrating a system 1000 for time transfer according to a first embodiment of the invention. The system 1000 for time transfer comprises an entangled photon transmitter 100, a first photon receiver 200, and a second photon receiver 300. In the first embodiment, the entangled photon transmitter 100 is located separate from the first photon receiver 200, and the second photon receiver 300.

[0144] [00164] The entangled photon transmitter 100 is a satellite. The first photon receiver 200 is an optical ground receiver, referred to as OGR1. The first photon receiver 200 comprises a first clock 600, also referred to as a grandfather clock. The second photon receiver 300 is also an optical ground receiver, referred to as 00R2. The second photon receiver 300 comprises a second clock 700, also referred to as a grandchild clock. The system 1000 for time transfer transfers time between the first clock 600 and the second 700 by adjusting either the first clock 600 or second clock 700 by a clock offset. Transferring time between the first clock 600 and second clock 700 means that the first clock 600 and the second clock 700 will have the same time. Transferring time between the first clock 600 and second clock 700 may also be referred to as transferring a time value between the first clock 600 and the second clock 700 or synchronizing the first clock 600 and the second clock. As mentioned above, the clocks in both OGRs discipline or control the timing systems of the respective OGRs.

[0145] [00165] To transfer time between the first clock 600 and the second clock 700, the satellite 100 sends a series of entangled photons to both the first OGR 200 and the second OGR 300. In the following embodiments, time is transferred between the first clock 600 (the grandfather clock) and the second clock 700 (the grandchild clock) by adjusting the second clock 700 by a clock offset. However, the following embodiments are not limited to such configurations. In the following embodiments, time can be transferred between the first clock 600 (the grandfather clock) and the second clock 700 (the grandchild clock) by adjusting the first clock 700 by a clock offset. It is noted that the terms "grandfather" clock and "grandchild" clock are merely to denote which clock is adjusted by the clock offset. Either of the first or second clock can be adjusted by the clock offset such that time is transferred between the first and second clocks and the first and second clocks are synchronized.

[0146] [00166] Each entangled photon in the series comprises a first photon 114 and a second photon 116, so that in the illustrated embodiment each entangled photon comprises an entangled photon pair. The time between the first clock 600 of the first OGR 200 and the second clock 700 of the second OGR 300 are transferred to each other based on the entangled photons that are transmitted from the satellite 100. As discussed in further detail below, the time between the first clock 600 and the second clock 700 are transferred by adjusting either the first clock 600 or the second clock 700 by a clock offset. Advantageously, transmitting entangled photons to the first OGR 200 and the second OGR 300 allows the two ground receivers to have the same time. Advantageously, transmitting entangled photons to the first OGR 200 and the second OGR 300 allows the two ground receivers to have the same time without the need for a clock on the satellite 100. This is different from the previous examples, such as Figures 1 -7, where the satellite 2 transmits a single photon to synchronise the satellite 2 with a single ground receiver 3.

[0147] [00167] When each of the OGRs receive their entangled photon, the OGRs determine a detection timestamp of when the entangled photon has been received by the OGR, in accordance with arrangements described above. In the illustrated embodiment in Figure 9, the first OGR 200 determines a first detection timestamp of when the first OGR 200 receives the first photon 114, and the second OGR 300 determines a second detection timestamp of when the second OGR 300 receives the second photon 116. However, the detection timestamp of when one OGR receives an entangled photon is usually different from when another OGR receives its entangled photon and therefore the OGRs generally will not have the same time on their clocks based on the detection timestamp alone. This is because of two main reasons: the entangled photons are received by the OGRs at different times due to time of flight differences due to asymmetrical distance from the satellite, and because a clock offset can be present. The clock offset may be present because a reference point between the first and second clock are different. For example, the reference point can be a zero second reference point of the first clock and second clock If the first clock and second clock have different zero second reference points, there clocks will be offset from each other. For example, a zero second reference point of the first clock of the first OGR could be 5 nanoseconds later than the zero second reference point of the second clock of the second OGR. This will result in first clock timestamping the entangled photon detections 5 nanoseconds later than the second clock, although they relate to the same entangled photon, or matched event. A clock offset may also be present because the entangled photons, although emitted at almost identical times due to spontaneous parametric down-conversion, are emitted at slightly different times. This difference between the emission timestamp of the first photon 114 and the emission timestamp of the second photon 116, is also herein referred to as a clock offset. Thus, the clock offset between the emission timestamps depends in part on a thickness of the non-linear crystals of an entangled photon source 110 of the entangled photon transmitter 100. The thickness of the non-linear crystals cause a non-simultaneous emission of entangled photons. These two different causes may both contribute to the total clock offset.

[0148] [00168] The first OGR 200 and the second OGR 300 have the same time of when the entangled photons are emitted from the satellite 100, which will be almost identical for all OGRs. However, they are not "exactly identical because there may be a clock offset between when the entangled photons are emitted from the satellite 100, due to the thickness of the non-linear crystals in the entangled photon source 110, and the difference in clock reference points. This is because the entangled photons share temporal correlations when the entangled photons are generated by the entangled photon source 110 of the satellite 100. For understanding, in an ideal environment, if one assumes that the non-linear crystals are infinitely thin, the link distance between the entangled photon source 110 and the OGRs would be identical and there would be no link loss. Consequently, even entangled photon emission would be detected at each OGR. This means that the first detection at the first OGR would correspond to the first detection at second OGR, and the second detection at the first OGR would correspond to the second detection at the second OGR, and so on. This means that the photon detections at each OGR would result from a pair of entangled photons emitted at the same time, hence the temporal correlation. However, in practice, some photons from the entangled photons are lost, i.e. not received by the OGR. Furthermore, each OGR may not receive a photon from the same pair of entangled photons. Therefore, the timestamps of when the photons are received would be different for each OGR. The clock offset between the two OGRs are therefore removed from either the first clock or second clock to carry out time transfer between the first and second clocks based on the difference between the first OGR and second OGR photon emission timestamps.

[0149] [00169] Accordingly, the system 1000 for time transfer removes the time of flight offset from the detection timestamp to obtain an emission timestamp The emission timestamp is when the entangled photons are emitted from the satellite 100. The emission timestamp for the first photon 114 and the second photon 116 are almost identical and temporally correlated.

[0150] [00170]Th The first OGR 200 and the second OGR 300 collects a set of emission timestamps from the series of entangled photons emitted by the satellite 100. The system 1000 for time transfer then further cross-correlates the set of first emission timestamps and the set of second emission timestamps to determine a clock offset between the set of first emission timestamps and the set of second emission timestamps. This can be repeated for each set of emission timestamps corresponding to a series of entangled photons to obtain a corresponding set of clock offsets. The set of clock offsets are then used to obtain a group clock offset. For example, an average of the set of clock offsets can be determined as the group clock offset. Afterwards, the first clock 600 or the second clock 700 is adjusted by the group clock offset. Consequently, the first clock 600 and the second clock 700 will share a common time, i.e. the same time.

[0151] [00171] In an example, the first clock 600 is a low quality clock. A low quality clock is typically a clock that is unable to provide a stable timing signal by itself. Characteristics of a low quality clock include inaccurate readings. For example, a low quality clock may inaccurately read the time as 12:01, when it is in fact 12:00. Another characteristic of a low quality clock is time drifting and aging. For example, for every 24 hours, the time may drift by 1 minute. This would result in the clock time increasing by 24 hours and 1 minute every true 24 hours. This is typically because low quality clocks are prone to environmental changes and effects. Low quality clocks include, but are not limited to, a quartz oscillator clock. Having said this, advantageously, low quality clocks are easier to integrate into existing systems due to their compactness.

[0152] [00172] In an example, the second clock 700 is a high quality clock. Advantageously, high quality clocks on the other hand have significantly improved accuracy and almost non-existent drifting. High quality clocks can also maintain accuracy readings on its own without the need for a separate reference time, or at least maintain accurate readings on its own for longer than low quality clocks. High quality clocks include, but are not limited to, atomic clocks (such as rubidium and caesium), and optical clocks. However, generally high quality clocks are large and bulky and generally only suitable for ground locations.

[0153] [00173] Accordingly, because of the size and weight of high quality clocks, high quality clocks are not suitable for satellite 100, which needs to meet Size, Weight, and Power (SWaP) requirements for deployment. Advantageously, the first embodiment of the invention provides a system for time transfer without the need for any clocks on a satellite 100. Advantageously, the first embodiment of the invention also provides accurate and economical time transfer by transferring time from a high quality clock to a low quality clock.

[0154] [00174] The time transfer system 1000 comprises a respective quantum communication channel 400 between the satellite 100 and each of the optical ground receivers 200, 300. The satellite 100 is configured to generate and transmit entangled photons to the first OCR 200 and the second OCR 300 via the quantum communication channels 400. The entangled photons comprise a first photon 114 and a second photon 116. The first photon 114 is sent from the satellite 100 to the first OGR 200. The second photon 116 is sent from the satellite 100 to the second OCR 300.

[0155] [00175] The first OCR 200 and the second OCR 300 can communicate via a classical communication channel 5011 Amongst other types of data, the classical communication channel 500 can be used to communicate various timestamps. Various timestamps include, but are not limited to, detection timestamps of when the entangled photons were received by the OGRs, and emission timestamps of when the entangled photons were emitted by the satellite 100.

[0156] [00176] Figure 10 is a schematic diagram illustrating an entangled photon transmitter 100 according to the first embodiment of the invention. The entangled photon transmitter 100 is a satellite 100. The satellite 100 comprises an entangled photons generator 110, an optical terminal 112, and a retroreflector 120. In an embodiment, the satellite 100 can be a low earth orbit satellite.

[0157] [00177]The entangled photons generator 110 is configured to generate and emit a series of entangled photons, wherein each entangled photons comprise a first photon 114 and a second photon 116. The series of entangled photons is more than one entangled photon. For example, the entangled photons generator 110 can generate and emit a series often entangled photons, this would result in ten first photons 114 and ten second photons 116. It is noted that illustrated embodiments show each of the entangled photons being a pair of entangled photons comprising a first photon 114 and a second photon 116. However, in other examples, the entangled photons may comprise more than two entangled photons, such as three entangled photons.

[0158] [00178]After the entangled photons generator 110 generates and emits the series of entangled photons, the series of entangled photons are sent to the optical terminal 112. Specifically, each entangled photons in the series are sent to the optical terminal 112. The optical terminal 112 is configured to transmit each photon of the entangled photons to the respective OGRs. For each entangled photons, in this case a pair of photons, the first photon 114 is transmitted to the first OGR 200 and the second photon 116 is sent to the second OGR 300. The first photon 114 and the second photon 116 are both transmitted from the satellite to the first OGR 200 and second OGR 300 via the quantum communication channels 400 [00179] The satellite 100 is non-stationary relative to the first OGR 200 and the second OGR 300, and therefore the first photon 114 and the second photon 116 will be detected at different times. Accordingly, the detection times and timestamps of the first photon 114 and the second photon 116 will be different. This is because of the time of flight offset within the detection timestamps. The time of flight offsets will generally be different for the first photon 114 and the second photon 116 due to asymmetrical distance between satellite 100 and the first and second OGRs 200, 300.

[0159] [00180] The entangled photon source 110 also does not generate and emit the first photon 114 and the second photon 116 at exactly the same time, but instead at almost the same time. Accordingly, there is a clock offset between when the first photon 114 is emitted from the optical terminal 112 and the when the second photon 116 is emitted from the optical terminal 112. Accordingly, there is a clock offset between the emission timestamp of the first photon 114 and the emission timestamp of the second photon 116, even after the time of flight offset is removed from both detection timestamps.

[0160] [00181] The first photon 114 can also be referred to as an idler photon and the second photon 116 can be referred to as a signal photon. The entangled photons are entangled by time energy. Optionally, the entangled photon can be entangled by any: polarisation, frequency, or time-bin.

[0161] It is noted that the illustrated figures in this disclosure shows photons suitable for polarisation encoding. However, the present disclosure is rot limited to polarisation encoding, and can be realised by other encoding methods and systems.

[0162] [00182]Th The entangled photon source 110 comprises a part of a time synchronisation system, as described in Figure 2A. In the first embodiment, the same principles as Figures 1 -7 may be used to remove the time of flight offset for each photon of the entangled photons sent from the satellite 100 to the OGRs. However, instead of the faint pulse laser system and the faint pulse electronics of Figures 1 -7, the entangled photons source 110 instead comprises entangled photon generation system and the entangled photon generation electronics. The entangled photon generation system and entangled photon generation electronics output an entangled photons beam, which comprises the first photon 114 and the second photon 116.

[0163] The first photon 114 is combined with a first synchronisation beam and the satellite 100 emits a first combined beam to the first OGR 200. The second photon 116 is combined with a second synchronisation beam and the satellite 100 emits a second combined beam to the second OGR 300. The first OGR 200 and the second OGR 300 thereafter proceed to determine the time of flight offset of the first photon 114 and second photon 116 in accordance with Figure 1 -7, as described above.

[0164] [00183] Figure 11 is a schematic diagram illustrating a first photon receiver according to the first embodiment of the invention. The first photon receiver 200 is an optical ground receiver OGR 200. The OGR1 comprises a telescope 210, a synchronisation transmitter and receiver 220, a quantum receiver system 230, a time-tagger system 240, a processor 250, a first clock interface 260, and a classical communications system 270.

[0165] [00184]Th The telescope 210 is configured to receive the first combined beam from the optical terminal 112 of the satellite 100. The first combined beam comprises the first photon 114 and the first synchronisation beam. Thereafter, the telescope 210, or any other equivalent part of the OGR, splits the first photon 114 and the first synchronisation beam from the first combined beam. Once the combined beam is split, the first photon 114 is detected by the quantum receiver system 230, and the first synchronisation beam is detected by the synchronisation transmitter and receiver 220.

[0166] [00185]Th The time-tagger system 240 timestamps when the first photon 114 is detected by the first OGR 200, also known as the first detection timestamp. Using the synchronisation laser method described with reference to Figures 1 -7, the processor 250 uses the first synchronisation beam to determine the time of flight offset, and determines the emission timestamp of the first photon 114 by removing the time of flight offset from the detection timestamp of the first photon 114, also referred to as the first emission timestamp. The first emission timestamp of the first photon 114 is sent to classical communications system 270, which comprises a classical communications interface to communicate the first emission timestamp from the first OGR 200 to the second OGR 300 via the classical communications channel 500.

[0167] [00186] Figure 12 is a detailed schematic diagram illustrating the first photon receiver according to the first embodiment of the invention. As mentioned above, the method of removing the time of flight offset from the first detection timestamp is the same method referred to in Figures 1 -7. Like the OGR of Figures 1 -7, the first OGR 200 of the time synchronisation system 1000 also comprises a dichroic mirror, decoding optical system, a single photon detector, a synchronisation pulse detector, a time tagger, a timing recovery computer and a first clock. In addition to the OGR of Figures 1 -7, the first OGR 200 additionally comprises a synchronisation pulse emitter.

[0168] [00187] Figure 13 is a schematic diagram illustrating a second photon receiver according to the first embodiment of the invention. The second photon receiver 300 is an optical ground receiver OGR 300. OGR2 comprises a telescope 310, a synchronisation transmitter and receiver 320, a quantum receiver system 330, a time-tagger system 340, a processor 350, a second clock interface 360, and a classical communications system 370. Apart from the second clock interface 370, the components of the second photon receiver 300 are identical to the first photon receiver 200. The second photon receiver 300 also additionally comprises a synchronisation pulse emitter.

[0169] [00188] The telescope 310 is configured to receive the second combined beam from the optical terminal 112 of the satellite 100. The second combined beam comprises the second photon 116 and the second synchronisation beam. Thereafter, the telescope 310, or any other equivalent part of the OGR, splits the second photon 116 and the second synchronisation beam from the second combined beam. Once the second combined beam is split, the second photon 116 is detected by the quantum receiver system 330, and the second synchronisation beam is detected by the synchronisation transmitter and receiver 320.

[0170] [00189] The time-tagger system 340 timestamps when the second photon 116 is detected by the second OGR 300, also known as the second detection timestamp. Using the synchronisation laser method described with reference to Figures 1-7, the processor 350 uses the second synchronisation beam to determine the time of flight offset, and determines the emission timestamp of the second photon 116 by removing the time of flight offset from the detection timestamp of the second photon 116, also referred to as the second emission timestamp.

[0171] [00190] The classical communications system 370 of the second OGR 300 receives the first emission timestamp from the first OGR 200. Alternatively, or in addition, the second emission timestamp of the second photon 116 can be sent to classical communications system 370, which comprises a classical communications interface to communicate the second emission timestamp from the second OGR 300 to the first OGR 200 via the classical communications channel 500.

[0172] [00191] Figure 14 shows a laser ranging system according to all embodiments of the invention.

[0173] Alternatively, or in addition, the time transfer system 1000 can determine the time of flight offset associated with and to be removed from the detection timestamps using a laser ranging system.

[0174] [00192]The laser ranging system comprises a satellite and an optical ground receiver. The satellite can be the satellite 100 mentioned in the arrangements and embodiments of the present disclosure. The optical ground receiver can be the optical ground receivers mentioned in the arrangements and embodiments of the present disclosure.

[0175] [00193]The OGR of the laser ranging system comprises a telescope, a sync receiver, a timetagger system, a clock system, a processor, and a sync transmitter. The satellite of the laser ranging system comprises a retroflector. The processor, also known as OGR computer, is to generate a known pattern signal encoded in on-off keying. According to an embodiment, the processor generates a non-return to zero on-off keying. The processor sends the known pattern to the sync transmitter of the OGR to transmit a laser ranging beam encoded with the on-off keying to the satellite. The sync transmitter thereafter emits the laser ranging beam to the satellite via the telescope. Consequently, the retroreflector of the satellite receives the laser ranging beam. The retroflector of the satellite sends back the laser ranging beam to the OGR as a reflected laser ranging beam.

[0176] [00194]The OGR receives the reflected laser ranging beam via its telescope and the sync receiver of the OGR obtains the reflected laser ranging beam The sync receiver sends the received reflected laser ranging beam to the time-tagger system, which saves, in memory, the timing of when the reflected laser ranging beam was received. The time-tagger system also saves, in memory, the timing of when the original laser ranging beam was emitted to the satellite.

[0177] [00195]The OGR computer thereafter compares the transmitted time of the original laser ranging beam and the received time of the reflected laser ranging beam. Specifically, the OGR computer determines the difference in the transmitted time of the original laser ranging beam and the received time of the reflected laser ranging beam. This is possible because both the original laser ranging beam and the reflected laser ranging beam are encoded with the known pattern signal encoded in on-off keying. The comparison determines a time of flight offset of the reflected laser ranging beam. The time of flight offset of the reflected laser ranging beam can be determined using method known pattern matching algorithms. The time of flight offset of the reflected laser ranging beam is double the time of flight offset for the detection timestamps of the entangled photons mentioned above. This is because the laser ranging system travels double the distance of the photons emitted by the satellite 100. Accordingly, to determine the time of flight offset of the detection timestamps of the entangled photons, the time of flight offset of the reflected laser ranging beam is halved.

[0178] [00196] It is noted that Figure 14 shows a laser ranging system only for a single OGR. However, all OCRs in the time transfer system 1000 can comprise the laser ranging system of Figure 14.

[0179] [00197]Advantageously, the retro-reflector geometry in a laser ranging system reduces the impact of satellite induced noise on our timing signals, and allows for a fast cross-correlation algorithm.

[0180] [00198] Figure 15 is a time diagram illustrating true emission times of entangled photons detected by the first photon receiver and the second photon receiver. A true emission time is when the entangled photons are emitted from the entangled photon source, and it will be understood that this is without any time of flight offsets and clock offsets. In other words, Figure 15 shows the times at which a series of entangled photons are transmitted by the satellite 100 (denoted by central line 0) to the first OGR 200 (denoted by bottom line -1) and the second OGR 300 (denoted by top line 1). However, as shown in Figure 15, the first photon 114 and the second photon 116 of entangled photons may not be received by both the first OGR 200 and the second OGR 300. This is because of lossy environmental conditions. In some instances, the first photon 114 will not be transmitted to the first OGR 200, and the second photon 116 will not be transmitted to the second OGR 300. In some instances, the first photon 114 will be transmitted to the first OGR 200, but the second photon 116 will not be transmitted to the second OGR 300. In some instances, the second photon 116 will be transmitted to the second OGR 300, but the first photon 114 will not be transmitted to the first OGR 200.However, sometimes both entangled photons will be transmitted to both the first OGR 200 and the OGR 300 and the first OGR 200 and second OGR 300 will detect the same pair of entangled photons. When the first OGR 200 and the second OGR 300 detect the same pair of entangled photons in the series of entangled photons, this is called a matched event. This is indicated in Figure 15 by a vertical line that connects the both the OGR 1 detection event dot on the bottom line -1 and the OGR 2 detection event dot on the top line 1. The time separation between the pair of entangled photons in the matched events (not shown in Figure 15) is the time of flight and clock offset between the first clock 600 at the first OGR 200 and the second clock 700 at the second OGR 300, this can be seen in Figure 16 and Figure 17.

[0181] [00199] Figure 16 is a time diagram illustrating detection timestamps of when the photons were received by the first photon receiver and the second photon receiver, including time of flight offsets and clock offsets. Figure 16 shows that the first OGR 200 detector, indicated by the detection events on the bottom line with -1 amplitude, detected the series of entangled photons later than the second OGR 300, indicated by the detection events on the top line with 1 amplitude. Both the detection timestamps of the first OGR 200 and the second OGR 300 comprise a time of flight offset and clock offset. For simplicity, the time of flight offset and the clock offset are jointly shown as a single offset TOF. The first time of flight offset TOF-B is greater than the second time of flight offset TOF-A in this case because the first OGR 200 was located further away from the satellite 100 than the second OGR 300 at the time when the entangled photons were emitted by the satellite 100.

[0182] [00200] The processor 250 of the first OGR 200 and the processor 350 of the second OGR 300 each determine the time of flight offset for each detection timestamp in the series of detection timestamps. This can be using the synchronisation laser system according to Figures 1 -7 or the time of flight ranging system according to Figure 14.

[0183] [00201]Advantageously, determining the time of flight offset factors in any variation in path length between the satellite and the two OGRs and therefore time synchronisation is suitable for systems where the position of the satellite may be inaccurate, or dynamic.

[0184] [00202] Figure 17 is a time diagram illustrating determined emission timestamps of photons received by the first photon receiver and the second photon receiver, from which time of flight offsets have been removed, but including clock offsets for all embodiments. The first emission timestamps determined by the first OGR 200 is delayed relative to the second emission timestamps determined by the second OGR 300. This is because the first photon 114 and second photon 116 have a clock offset when generated by the entangled photons source 110. As a result, the matched events are each separated by the clock offset. The clock offset is present mainly due to differences between respective reference points of the first and second clocks, and also because the first photon 114 and the second photon 116 are not transmitted at exactly the same time, but almost the same time, as explained above. To determine the clock offset, firstly, the time of flight offsets are subtracted from the first and second detection timestamps to produce first and second emission timestamps, as discussed in relation to Figure 16. Secondly, the first emission timestamps and the second emission timestamps are cross correlated to determine the clock offset. Methods of cross correlation include a numerical discrete cross-correlation methodology or an arrival time-difference histogram approach.

[0185] [00203]Advantageously, a group clock offset for all matched events can be calculated to improve the accuracy of the clock offset. To determine a group clock offset, a plurality of clock offsets are averaged, wherein the plurality of clock offsets are obtained from cross correlating a plurality of first emission timestamps and a plurality of second emission timestamps. It is noted that a variation the group clock offset can be monitored. Variations of the group clock offset can be monitored by plotting the change of group clock offset with respect to time. The plot will also give a measure of frequency drift of the group clock offset. Monitoring the variations can be used to determine a frequency variation between the first clock 600 and the second clock 700.

[0186] [00204]Th The cross correlation can be executed by the processor 350 in the second OGR 300. The first OGR 200 communicates the first emission timestamps from the first time-tagger system 240 to the second OGR 300 via the classical communication channel 500. Once the second OGR 300 receives the first emission timestamps, the processor 350 in the second OGR 300 cross correlates the first emission timestamps with the second emission timestamps stored in the time-tagger system 340 in the second OGR 300.

[0187] [00205] Alternatively, the cross correlation can be executed by the processor 250 in the first OGR 200. In this arrangement, the second OGR 300 communicates the second emission timestamps from the second time-tagger system 340 to the first OGR 200 via the classical communication channel 500. Once the first OGR 200 receives the second emission timestamps, the processor 250 in the first OGR 200 cross correlates the second emission timestamps with the first emission timestamps stored in the time-tagger system 240 in the first OGR 200.

[0188] [00206] Figure 18 is a cross correlation output diagram illustrating the cross correlation for different values of the clock offset between the first emission timestamps received by the first photon receiver and the second emission timestamps received by the second photon receiver for all embodiments. Figure 18 shows that cross correlation outputs have a maximum corresponding to a clock offset of 5 nanoseconds, indicating that this is the correct clock offset.

[0189] [00207]Advantageously, the combination of utilising an entangled photon transmitter and removing the time of flight from the detection timestamps at the photon receivers enable time transfer between two clocks whilst removing the need for a clock at the entangled photon transmitter. That is, there is no need for a high accuracy clock, such as a master, or reference, clock, as part of the time transfer system.

[0190] [00208]Th The combination of utilising an entangled photon transmitter and removing the time of flight from the detection timestamps at the photon receivers may be further advantageous if the entangled photon transmitter is non-stationary, for example on a satellite, and is therefore required to be light and compact. The combination of a dual downlink entangled photon transmitter with a time synchronisation laser system, or time of flight ranging system, removes the need for a high-quality clock, or any clock, on-board the entangled photon transmitter. This improves the SWaP properties of the entangled photon transmitter.

[0191] [00209]Figure 19 is a schematic diagram illustrating a second time transfer system 2000 according to the second embodiment of the invention. The time transfer system 2000 also comprises the entangled photon transmitter 100, the first photon receiver 200, and the second photon receiver 300. In the second embodiment, the second photon receiver 300 is located separate from the entangled photon transmitter 100 and the first photon receiver 200. The entangled photon transmitter 100 and the first photon receiver 200 are co-located.

[0192] [00210] In the second embodiment, the entangled photon transmitter 100 and the first photon receiver 200 are located on a satellite; and the second photon receiver 300 is an optical ground receiver. Because the entangled photon transmitter 100 and the first photon receiver 200 are co-located, the first photon receiver comprises a quantum heralding scheme 118 that detects the first photon 114 directly from the entangled photon source 110. The first detection timestamp of the first photon 114 can be directly sent to the time-tagger system 240. Alternatively, the time of flight offset of the first detection timestamp can be estimated to be non-existent.

[0193] [00211] Aside from the features mentioned above, the system and method of time transfer of the second embodiment are the same as the first embodiment.

[0194] [00212] Figure 20 is a schematic diagram illustrating a third time transfer system according to the third embodiment of the invention. The time transfer system 3000 also comprises the entangled photon transmitter 100, the first photon receiver 200, and the second photon receiver 300. In the third embodiment, the second photon receiver 300 and the entangled photon transmitter 100 are located separate from the first photon receiver 200.

[0195] [00213] In the third embodiment, the first photon receiver 200 is located on a satellite; and the second photon receiver 300 is an optical ground receiver, and the entangled photon transmitter 100 is located on the optical ground receiver. Because the entangled photon transmitter 100 and the second photon receiver 300 are co-located, the second photon receiver comprises a quantum heralding scheme 118 that detects the second photon 116 directly from the entangled photon source 110. The second detection timestamp of the second photon 116 can be directly sent to the time-tagger system 340. Alternatively, the time of flight offset of the second detection timestamp can be estimated to be non-existent [00214]Aside from the features mentioned above with respect to the third embodiment, the system and method of time transfer of the third embodiment are the same as the first embodiment.

[0196] [00215] Figure 21 is flow chart illustrating a method of time transfer 800 for all embodiments.

[0197] [00216] In step 810, the method 800 comprises, at an entangled photon transmitter, generating a series of entangled photons, wherein each entangled photons comprise a first photon and a second photon.

[0198] [00217] In step 820, the method 800 comprises: at the entangled photon transmitter, for each entangled photons, transmitting the first photon to a first photon receiver comprising a first clock; at the entangled photon transmitter, for each entangled photons, transmitting the second photon to a second photon receiver comprising a second clock.

[0199] [00218] In step 832, the method 800 comprises, at a first photon receiver, for each of received ones of the entangled photons, determining a first detection timestamp of when the first photon was received by the first photon receiver.

[0200] [00219] In step 834, the method 800 comprises, at the first photon receiver, for each entangled photons, determining a first emission timestamp of when the received first photon was transmitted by the entangled photon transmitter by determining a first time of flight offset of the first detection timestamp and removing the first time of flight offset from the first detection timestamp.

[0201] [00220] In step 836, the method 800 comprises, at the second photon receiver, for each of received ones of the entangled photons, determining a second detection timestamp of when the second photon was received by the second photon receiver.

[0202] [00221] In step 838, the method 800 comprises, at the second photon receiver, for each entangled photons, determining a second emission timestamp of when the received second photon was transmitted by the entangled photon transmitter by determining a second time of flight offset of the second detection timestamp and removing the second time of flight offset from the second detection timestamp.

[0203] [00222] In step 840, the method 800 comprises, communicating, for each entangled photons, the first emission timestamp to the second photon receiver, or the second emission timestamp to the first photon receiver.

[0204] [00223] In step 850, the method 800 comprises, determining, for each entangled photons, a clock offset between the first emission timestamp and the second emission timestamp by calculating a cross-correlation between the first emission timestamp and the second emission 30 timestamp [00224]Optionally, in step 860, the method 800 comprises, determining, a group clock offset based on each clock offset of the entangled photons in the series of entangled photons.

[0205] [00225] In step 870, the method 800 comprises, transferring time between, or synchronising, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset, or optionally by the group clock offset.

[0206] [00226]Advantageously, in all embodiments, the tight temporal correlations achieved through production of pairs of entangled photons allows for the possibility of sub nanosecond accuracy thus allowing the development of future networks, including quantum networks [00227]Advantageously, in all embodiments, the time transfer system provides the entangled photon transmitter 100 with a one-way entanglement distribution architecture, which allows for time transfer performance improvements as one-way entanglement distribution allows for higher e-bit detection rates, thus reducing the impact of noise on the time transfer system.

[0207] Advantageously, the one-way entanglement distribution has a higher e-bit detection rate than bidirectional entanglement distribution. This is because one-way entanglement distribution only requires two detection events to be recorded in the time transfer system, whereas a bidirectional entanglement distribution requires four detection events to be recorded to enable time transfer.

[0208] [00228]Advantageously, in all embodiments, the time transfer system provides a dual downlink in a single configuration, i.e. the entangled photon transmitter communicates with the photon receivers but the photon receivers do not need to send any information back to the satellite. This is advantageous over other systems, where the entangled photon source and the photon receivers are in a two-way configuration, and are required to communicate one after each other to obtain the clock offset, i.e. a signal photon to the first photon receiver and an idler photon to a second receiver, then signal photon to second photon receiver and idler photon to first photon receiver. Such other systems provide an inefficient protocol and are less compact because of presence of EPS to dual optical terminals.

[0209] [00229] In the embodiments and arrangements described herein, the quantum beam is encoded using the polarisation encoded BB84 protocoL In other examples, different encoding protocols may be used. For example, encoding protocols using other encoding techniques, such as time-bin encoding, or different QKD protocols, such as CV QKD, or different quantum protocols, such as quantum digital signatures, may additionally or alternatively be used in the described embodiments and examples.

[0210] [00230] In the embodiments and arrangements described herein the system is a quantum key distribution system. In other examples other cryptographic items could be distributed/delivered in addition to, or as an alternative to, encryption keys. Examples of such other cryptographic items include cryptographic tokens, cryptographic coins, or value transfers.

[0211] [00231] In the embodiments and arrangements described herein, it is assumed that the components of the system are of sufficiently high specification to allow the time-transfer to take place. This refers to the jitter in the system, resolution of the detection and the efficiency of detection of the pulses. The precise specifications required will depend upon the characteristics of the system in any specific implementation.

[0212] [00232] In the embodiments and arrangements described above, it is assumed that a constellation approach is to deliver a continuous service, as the weak quantum optical signals may be affected by loss and environmental conditions. For example, due to background counts and dark counts from single photon detectors. A constellation approach allows for the hold over times of ground-based clock systems, which have lower performance characteristics, for example clock drifts greater than 1 micro second for clock holdover periods less than 1 day, to be maintained to sufficient accuracy required by end users.

[0213] [00233] In the embodiments and arrangements described above, the entangled photons can be polarisation entangled or frequency entangled. The satellites and optical ground receivers can monitor correlations in the polarisation states, or frequency, of the entangled photons. In addition, monitoring the polarisation states, or frequency, of the entangled photons allows monitoring of the quantum bit error rate of the series of entangled photons. Advantageously, monitoring the quantum bit error rate of the series of entangled photons allows the time transfer systems of the present embodiments and arrangements to detect intercept-resend attacks, for example, in a QKD system.

[0214] [00234] In the embodiments described above, at least one of the entangled photon transmitter, the first photon receiver, or the second photon receiver can be non-stationary. In another embodiment, the first photon receiver and second photon receiver can be stationary and the entangled photon transmitter can be non-stationary. In another embodiment, the second photon receiver is stationary and the entangled photon transmitter and the first photon receiver can be non-stationary. In another embodiment, the first photon receiver, second photon receiver and the entangled photon transmitter can be all non-stationary. As long as the time of flight offset can be calculated, time transfer can be achieved.

[0215] [00235] Figure 22 shows a computing system 5000, on which any of the above-described methods may be performed. In particular, the Computing system 5000 may comprise a single computing device or components such as a laptop, tablet, desktop or other computing device. Alternatively functions of system 5000 may be distributed across multiple computing devices.

[0216] [00236]Th The Computing system 5000 may include one or more controllers such as controller 5005 that may be, for example, a central processing unit processor (CPU), a graphics processing unit (GPU) a chip or any suitable processor or computing or computational device such as an FPGA mentioned, an operating system 5015, a memory 5020 storing executable code 5025, storage 5030 which may be external to the system or embedded in memory 5020, one or more input devices 5035 and one or more output devices 5040.

[0217] [00237] One or more processors in one or mare controllers such as controller 5005 may be configured to carry out any of the methods described here. For example, one or more processors within controller 5005 may be connected to memory 5020 storing software or instructions that, when executed by the one or more processors, cause the one or more processors to carry out a method according to some embodiments of the present invention. Controller 5005 or a central processing unit within controller 5005 may be configured, for example, using instructions stored in memory 5020, to perform the method as described above.

[0218] [00238] Input devices 5035 may be or may include a mouse, a keyboard, a touch screen or pad or any suitable input device. It will be recognized that any suitable number of input devices may be operatively connected to computing system 5000 as shown by block 5035. Output devices 5040 may include one or more displays, speakers and/or any other suitable output devices. It will be recognized that any suitable number of output devices may be operatively connected to computing system 5000 as shown by block 5040. The input and output devices may for example be used to enable a user to select information, e.g., images and graphs as shown here, to be displayed.

[0219] [00239] In the embodiments described above, all or parts of the method may be performed by a server. The server may comprise a single server or network of servers. In some examples, the functionality of the server may be provided by a network of servers distributed across a geographical area, such as a worldwide distributed network of servers, and a user/operator of the method may be connected to an appropriate one of the network servers based upon, for example, a user location.

[0220] [00240]Th The embodiments described above are fully automatic. In some examples a user or operator of the system may manually instruct some steps of the method to be carried out [00241] In the described embodiments of the invention parts of the system may be implemented as a form of a computing and/or electronic device. Such a device may comprise one or more processors which may be microprocessors, controllers or any other suitable type of processors for processing computer executable instructions to control the operation of the device in order to gather and record routing information. In some examples, for example where a system on a chip architecture is used, the processors may include one or more fixed function blocks (also referred to as accelerators) which implement a part of the method in hardware (rather than software or firmware). Platform software comprising an operating system or any other suitable platform software may be provided at the computing-based device to enable application software to be executed on the device.

[0221] [00242]Various functions described herein can be implemented in hardware, software, or any combination thereof If implemented in software, the functions can be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media may include, for example, computer-readable storage media. Computer-readable storage media may include volatile or non-volatile, removable or non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. A computer-readable storage media can be any available storage media that may be accessed by a computer. By way of example, and not limitation, such computer-readable storage media may comprise RAM, ROM, EEPROM, flash memory or other memory devices, CD-ROM or other optical disc storage, magnetic disc storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Disc and disk, as used herein, include compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and blu-ray disc (BD). Further, a propagated signal is not included within the scope of computer-readable storage media Computer-readable media also includes communication media including any medium that facilitates transfer of a computer program from one place to another. A connection, for instance, can be a communication medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of communication medium. Combinations of the above should also be included within the scope of computer-readable media.

[0222] [00243]Alternatively, or in addition, the functionality described herein can be performed, at least in part, by one or more hardware logic components. For example, and without limitation, hardware logic components that can be used may include Field-programmable Gate Arrays (FPGAs), Program-specific Integrated Circuits (ASICs), Program-specific Standard Products (ASSPs), System-on-a-chip systems (SOCs), Complex Programmable Logic Devices (CPLDs), etc. [00244] Although illustrated as a single system, it is to be understood that a computing device may be a distributed system. Thus, for instance, several devices may be in communication by way of a network connection and may collectively perform tasks described as being performed by the computing device. Although illustrated as a local device it will be appreciated that the computing device may be located remotely and accessed via a network or other communication link (for example using a communication interface).

[0223] [00245]The term 'computer is used herein to refer to any device with processing capability such that it can execute instructions. Those skilled in the art will realise that such processing capabilities are incorporated into many different devices and therefore the term 'computer' includes PCs, servers, mobile telephones, personal digital assistants and many other devices.

[0224] [00246]Those skilled in the art will realise that storage devices utilised to store program instructions can be distributed across a network. For example, a remote computer may store an example of the process described as software. A local or terminal computer may access the remote computer and download a part or all of the software to run the program. Alternatively, the local computer may download pieces of the software as needed, or execute some software instructions at the local terminal and some at the remote computer (or computer network).

[0225] Those skilled in the art will also realise that by utilising conventional techniques known to those skilled in the art that all, or a portion of the software instructions may be carried out by a dedicated circuit, such as a DSP, programmable logic array, or the like.

[0226] [00247] It will be understood that the benefits and advantages described above may relate to one embodiment or may relate to several embodiments. The embodiments are not limited to those that solve any or all of the stated problems or those that have any or all of the stated benefits and advantages. Variants should be considered to be included into the scope of the invention.

[0227] [00248]Any reference to an item refers to one or more of those items. The term 'comprising' is used herein to mean including the method steps or elements identified, but that such steps or elements do not comprise an exclusive list and a method or apparatus may contain additional steps or elements.

[0228] [00249]As used herein, the terms "component" and "system" are intended to encompass computer-readable data storage that is configured with computer-executable instructions that cause certain functionality to be performed when executed by a processor. The computer-executable instructions may include a routine, a function, or the like It is also to be understood that a component or system may be localized on a single device or distributed across several devices.

[0229] [00250]Further, as used herein, the term "exemplary" is intended to mean "serving as an illustration or example of something" [00251] Further, to the extent that the term "includes" is used in either the detailed description or the claims, such term is intended to be inclusive in a manner similar to the term "comprising" as "comprising" is interpreted when employed as a transitional word in a claim.

[0230] [00252]Th The figures illustrate exemplary methods. VVhile the methods are shown and described as being a series of acts that are performed in a particular sequence, it is to be understood and appreciated that the methods are not limited by the order of the sequence. For example, some acts can occur in a different order than what is described herein. In addition, an act can occur concurrently with another act. Further, in some instances, not all acts may be required to implement a method described herein.

[0231] [00253] Moreover, the acts described herein may comprise computer-executable instructions that can be implemented by one or more processors and/or stored on a computer-readable medium or media. The computer-executable instructions can include routines, sub-routines, programs, threads of execution, and/or the like. Still further, results of acts of the methods can be stored in a computer-readable medium, displayed on a display device, and/or the like.

[0232] [00254] The order of the steps of the methods described herein is exemplary, but the steps may be carried out in any suitable order, or simultaneously where appropriate. Additionally, steps may be added or substituted in, or individual steps may be deleted from any of the methods without departing from the scope of the subject matter described herein. Aspects of any of the examples described above may be combined with aspects of any of the other examples described to form further examples without losing the effect sought.

[0233] [00255] It will be understood that the above description of a preferred embodiment is given by way of example only and that various modifications may be made by those skilled in the art.

[0234] What has been described above includes examples of one or more embodiments. It is, of course, not possible to describe every conceivable modification and alteration of the above devices or methods for purposes of describing the aforementioned aspects, but one of ordinary skill in the art can recognize that many further modifications and permutations of various aspects are possible. Accordingly, the described aspects are intended to embrace all such alterations, modifications, and variations that fall within the scope of the appended claims.

Claims

1. Claims 1 A method of time transfer between a first clock and a second clock, the method comprising: a) at an entangled photon transmitter, generating a series of entangled photons, wherein each entangled photons comprise a first photon and a second photon; b) at the entangled photon transmitter, for each entangled photons, transmitting the first photon to a first photon receiver comprising the first clock; c) at the entangled photon transmitter, for each entangled photons, transmitting the second photon to a second photon receiver comprising the second clock; d) at a first photon receiver, determining a series of first detection timestamps of when ones of the first photons were received by the first photon receiver; e) at the first photon receiver, determining a series of first emission timestamps of when the received first photons were transmitted by the entangled photon transmitter by: determining a first time of flight offset of each first detection timestamp; and removing the first time of flight offset from each first detection timestamp; f) at the second photon receiver, determining a series of second detection timestamps of when ones of the second photons were received by the second photon receiver; g) at the second photon receiver, determining a series of second emission timestamps of when the received second photons were transmitted by the entangled photon transmitter by: determining a second time of flight offset of each second detection timestamp; and removing the second time of flight offset from each second detection timestamp; h) communicating, the series of first emission timestamps to the second photon receiver, or the series of second emission timestamps to the first photon receiver; i) determining, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; j) transferring time between the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

2. 2 A method according to claim 1, wherein the method further comprises: determining, a plurality of clock offsets by repeating steps a) to i) for a corresponding plurality of series of entangled photons; determining, a group clock offset, wherein the group clock offset is an average of the plurality of clock offsets; and transferring time between the first clock and the second clock by adjusting either the first clock or second clock by the group clock offset.

3. 3 A method according to any preceding claim, wherein the entangled photons share temporal correlations when the entangled photons are generated by the entangled photon transmitter.

4. 4 A method according to any preceding claim, wherein the entangled photons are a pair of entangled photons.

5. A method according to any preceding claim, wherein the first photon is an idler photon and the second photon is a signal photon.

6. 6 A method according to any preceding claim, wherein the plurality of photons are entangled by time energy, polarisation, frequency, or time-bin

7. A method according to any preceding claim, wherein determining the detection timestamp of when a photon was received by the photon receiver comprises: receiving the photon through a telescope; detecting the photon via a quantum receiver system; demultiplexing the photon from a sync laser; and recording a detection event of the photon with a fimetagger.

8. A method according to any preceding claim, wherein determining the emission timestamps comprises performing a time synchronisation process to remove time of flight offsets for each photon receiver to calculate estimates of when each single photon was emitted from the entangle photon source.

9. A method according to any preceding claim, wherein removing the time of flight offset from the detection timestamps provides distance synchronisation between the first photon receiver and the second photon receiver.

10 A method according to any preceding claim, wherein the entangled photon transmitter comprises a synchronisation laser system and determining the time of flight offset comprises using the synchronisation laser system.

11 A method according to claim 8, wherein using the synchronisation laser system comprises: transmitting, by a photon receiver, using a telescope, a sync pattern to a retroreflector co-located with the entangled photon transmitter; returning, by the retroreflector, the sync pattern to the photon receiver; receiving, by a sync detector system, the sync pattern, wherein the sync detector system is co-located with the photon receiver by demultiplexing the sync pattern; determining, by the sync detector system, a delay in receiving the sync pattern to determine the time of flight offset

12 A method according to any preceding claim, wherein the photon receivers comprise a time of flight ranging system and determining the time of flight offset comprises: transmitting, by the photon receiver, a laser ranging beam from the photon receiver to the entangled photon source, wherein the laser ranging beam is encoded with a predetermined pattern signal; reflecting, by the entangled photon source, the laser ranging beam as a reflected laser ranging beam; receiving, by the photon receiver, the reflected laser ranging beam; comparing, by the photon receiver, a transmitted time of the original laser ranging beam and a received time of the reflected laser ranging beam, based on the predetermined pattern signal, to determine a time of flight offset of the reflected laser ranging beam; and determining, by the photon receiver, the time of flight offset of the detection timestamp by halving the time of flight offset of the reflected laser ranging beam.

13 A method according to any preceding claim, wherein the first photon receiver sends the first time of flight offset to the second photon receiver.

14 A method according to claim 13, wherein determining, for each entangled photons, a clock offset between the first emission timestamp and the second emission timestamp is at the second photon receiver

15 A method according to any preceding claim, wherein the second photon receiver sends the second time of flight offset to the first photon receiver.

16 A method according to claim 15, wherein determining, for each entangled photons, a clock offset between the first emission timestamp and the second emission timestamp is at the first photon receiver

17 A method according to any preceding claim, wherein the second photon receiver and the first photon receiver communicate the first emission timestamp or the second emission timestamp via a classical communication channel.

18 A method according to any preceding claim, wherein the cross-correlation comprises identifying matched events between the first time of flight offset and the second time of flight offset, wherein the matched events are offset by the clock offset.

19 A method according to any preceding claim, wherein the method further comprises determining a variation in the clock offset over time to determine frequency variations in between the first clock and the second clock.

A method according to any preceding claim, wherein the entangled photon transmitter is located separate from the first photon receiver and the second photon receiver.

21. A method according to claim 20, wherein: the entangled photon transmitter is located on a satellite and the first photon receiver and the second photon receiver are optical ground receivers.

22 A method according to any of claims 1 -19, wherein the second photon receiver is located separate from the entangled photon transmitter and the first photon receiver.

23 A method according to claim 6, wherein: the entangled photon transmitter and the first photon receiver are located on a satellite; and the second photon receiver is an optical ground receiver.

24 A method according to any of claims 1 -19, wherein the second photon receiver and the entangled photon transmitter are located separate from the first photon receiver.

A method according to claim 8, wherein: the first photon receiver is located on a satellite; and.the second photon receiver is an optical ground receiver, and the entangled photon transmitter is located on the optical ground receiver.

26 A method according to any preceding claim, wherein the clocks discipline the timing systems of the photon receivers.

27 A method according to any preceding claim, wherein the first clock is a child clock and the second clock is a parent clock, wherein child clock is adjusted to share a common time with the parent clock.

28 A method according to any preceding claim, wherein the first clock is a low quality clock and the second clock is a high quality clock.

29. A method according to any preceding claim, wherein the entangled photons are polarisation entangled or frequency entangled.

A method according to claim 11, wherein the method further comprises monitoring correlations in the polarisation states, or frequency, of the entangled photons.

31 A method according to claim 12, wherein the quantum bit error rate of the series of entangled photons are monitored, based on the correlations in the polarisation states or frequency, to detect intercept-resend attacks.

32. A method according to any preceding claim, wherein the method further comprises repeating steps of the preceding claim to transfer time between the first clock or second clock, with a third photon receiver comprising a third clock.

33. A system for time transfer between a first clock and a second clock, the system comprising.an entangled photon transmitter configured to: generate a series of entangled photons, wherein each entangled photons comprise a first photon and a second photon; and transmit, for each entangled photons, the first photon to a first photon receiver comprising the first clock; and transmit, for each entangled photons, the second photon to a second photon receiver comprising the second clock; the first photon receiver comprising the first clock, the first photon receiver configured to: determine, a series of first detection timestamps of when ones of the first photons were received by the first photon receiver; and determine, a series of first emission timestamps of when the received first photon were transmitted by the entangled photon transmitter by: determining a first time of flight offset of the first detection timestamp; and removing the first time of flight offset from the first detection timestamp; the second photon receiver comprising the second clock, the second photon receiver configured to: determine, a series of second detection timestamps of when ones of the second photons were received by the second photon receiver; and determine, a series of second emission timestamps of when the received second photons were transmitted by the entangled photon transmitter by: determining a second time of flight offset of the second detection timestamp; and removing the second time of flight offset from the second detection timestamp; and the system being configured to communicate, the series of first emission timestamps to the second photon receiver, or the series of second emission timestamps to the first photon receiver; determine, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and transfer time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

34 A method of time transfer between a first clock and a second clock, at an entangled photon transmitter in a time synchronisation system, the method comprising.a) generating a series of entangled photons, wherein each entangled photons comprise a first photon and a second photon; b) for each entangled photons, transmitting the first photon to a first photon receiver comprising the first clock; c) for each entangled photons, transmitting the second photon to a second photon receiver comprising the second clock; d) communicating, a series of first emission timestamps to the second photon receiver, or a series of second emission timestamps to the first photon receiver; e) determining, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and f) transferring time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

35. A system for time transfer between a first clock and a second clock, the system comprising an entangled photon transmitter configured to: generate a series of entangled photons, wherein each entangled photons comprise a first photon and a second photon; transmit, for each entangled photons, the first photon to a first photon receiver comprising the first clock; and transmit, for each entangled photons, the second photon to a second photon receiver comprising the second clock; communicate, a series of first emission timestamps to the second photon receiver, or a series of second emission timestamps to the first photon receiver; determine, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and transfer time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

36 A method of time transfer between a first clock and a second clock, at a first photon receiver comprising the first clock in a time synchronisation system, the method comprising: a) at a first photon receiver, determining a series of first detection timestamps of when first photons were received by the first photon receiver; b) at the first photon receiver, determining a series of first emission timestamps of when the first photons were transmitted by an entangled photon transmitter by determining a first time of flight offset of the first detection timestamp and removing the first time of flight offset from the first detection timestamp, c) communicating, the series of first emission timestamps to a second photon receiver, or a series of second emission timestamps to the first photon receiver; d) determining, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and e) transferring time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

37 A system for time transfer between a first clock and a second clock, the system comprising a first photon receiver comprising the first clock, the first photon receiver configured to: determine, a series of first detection timestamps of when first photons were received by the first photon receiver; determine, a series of first emission timestamps of when the first photons were transmitted by the entangled photon transmitter by: determining a first time of flight offset of the first detection timestamp; and removing the first time of flight offset from the first detection timestamp; communicate, the series of first emission timestamps to a second photon receiver, or the series of second emission timestamps to the first photon receiver, determine, a clock offset between the series of first emission timestamps and the series of second emission timestamps by calculating a cross-correlation between the series of first emission timestamps and the series of second emission timestamps; and transfer time between, the first clock and the second clock by adjusting either the first clock or second clock by the clock offset.

38 A computer-readable medium comprising code or computer instructions stored thereon, which when executed by a processor, causes the processor to perform the method according to any one of claims 1 to 32, 34, and 36.