CN113162767B - Heterodyne measurement-based four-state quantum key distribution method and system - Google Patents

Abstract

The invention provides a heterodyne measurement-based four-state quantum key distribution method and a heterodyne measurement-based four-state quantum key distribution system. And after the encoding of the transmitting and receiving parties is finished, performing classical error correction, calculating the security key rate in a privacy amplification link by adopting a key rate calculation method based on convex optimization and dual problems, performing privacy amplification based on the calculated security key rate, and finally obtaining the security key. The invention reduces the difficulty of phase precision preparation and phase feedback; on the other hand, the system has few types of sending signal light and is easy to prepare, the system is simplified, the safe transmission distance and the safe key rate of other continuous variable quantum key distribution systems can be surpassed, and the key distribution with simplicity, safety, efficiency and longer distance is realized.

Description

A four-state quantum key distribution method and system based on heterodyne measurement

technical field

The invention relates to the field of quantum key distribution, in particular to a four-state quantum key distribution method and system based on heterodyne measurement.

Background technique

Quantum key distribution combined with one-time pad technology can realize unconditionally secure and secure communication in information theory. When the confidentiality of the existing classical cryptosystem is threatened by the parallel computing ability of quantum computers, quantum key distribution becomes an optimal solution.

The discrete variable quantum key distribution proposed earlier needs to use a certain degree of freedom of single photon discretization, so it is constrained by the problems of large single photon channel loss and insufficient accuracy of measurement equipment, and the final security key rate is not enough to meet the existing communication needs. The subsequently proposed continuous variable quantum key distribution based on Gaussian modulation can theoretically use continuous degrees of freedom to carry more than one bit of information; using interferometry with strong light, each signal light can generate codeable data. Therefore, in a short distance, the security key rate of the continuous variable quantum key distribution has the ability to exceed the security key rate of the discrete variable quantum key distribution. In addition, the equipment required for continuous variable quantum key distribution is basically the same as that used in the existing optical communication system, and the distribution system is easier to merge with the existing optical communication system, so it is more effective than discrete variable quantum key distribution in the metropolitan area. Using foreground, it is easier to achieve.

However, the security of continuous variable quantum key distribution has been highly dependent on the condition that the regular component of the light pulse must be a continuous Gaussian distribution, because the continuous Gaussian distribution makes the overall quantum state of the distribution system have a mathematically strong symmetry-U(n) Symmetry (symmetry of n-dimensional unitary matrices). Various synchronization and feedback methods for continuous variable quantum key distribution also often require the data to have a Gaussian distribution before they can be implemented. However, although Gaussian modulation can theoretically make the regular component conform to the continuous Gaussian distribution, in practice the continuous Gaussian distribution cannot be prepared, and the Gaussian distribution can only be discretized. However, there must be enough discretized different signal states, and dozens of them are often required to build the symmetry allowed by the error. In addition, accurate measurements are required to calculate the true covariance and thus obtain a credible key ratio. These experimental techniques are immature, so the error estimation of security is very large, which leads to the fact that the key rate can only exceed the discrete variable quantum key distribution in a short distance, and quickly decays to 0 in a long distance.

Although many technicians in related fields consider sending fewer types of signal states to realize a discretely modulated continuous variable key distribution system, fewer signal states mean that the U(n) symmetry brought about by Gaussian modulation is destroyed. The distribution system loses the security protected by this symmetry. Most of the discrete modulation schemes either assume that the channel is a linear channel to limit the attacker's attack methods, or assume that Gaussian attack is the attacker's optimal attack method, so that the related security proof of Gaussian modulation is used again. In the face of discrete modulation, this assumption can only approach the lower limit of the real safe coding rate well when the light intensity tends to 0 in the mathematical proof. However, the light intensity of the signal light used in actual distribution cannot be so small, otherwise the transmission distance will be obviously limited; but the light intensity is not small enough, which will cause the lower limit to be too loose, and the code rate will quickly decay to 0, which will eventually lead to the difference between the code rate and the transmission. The distances are all low, not even close enough to go beyond discrete-variable quantum key distribution.

In practice, the existing continuous variable quantum key distribution system usually needs to jointly modulate the amplitude (amplitude) and phase of the pulse in order to be able to modulate the signal state to the state where the key information is encoded, which makes the operation more complicated. At the same time, the continuous variable quantum key distribution system usually uses a continuous laser with at least two intensity modulators to realize the preparation of pulses. There are many devices and it is easy to introduce a lot of noise; the actual voltage instability is not conducive to maintaining a continuous laser with stable intensity. , and continuous light chopping into pulses is extinction, which will waste a lot of energy. The phase feedback is a technical difficulty in practice. In the continuous variable quantum key distribution system, it is necessary to obtain the phase compensation value through complex detection and calculation, and then act on the relevant equipment of the system to make the signal state and the local oscillator light. Maintaining a fixed phase difference has poor real-time performance for high-speed pulses; or reducing the environmental changes that cause phase drift as much as possible, but it cannot essentially eliminate phase drift.

Contents of the invention

)，而仅固定信号光之间的相位差，即可实现接收端最大程度上的分辨，信号光和本振光之间相位差只影响数据后处理的操作，但并不降低成码率。脱离上述限制后，本发明降低了相位精准制备的难度，同时不需要在测量过程中不断计算相位补偿并作用在系统的相关设备上，降低了相位反馈的难度；另一方面，我们的系统发送信号光种类少且易于制备，简化了系统，减少了复杂设备引入的噪声，能够超越其他连续变量量子密钥分发系统的安全传输距离与安全密钥率，实现更简易、更安全、更高效以及更远距离的密钥分发。Purpose of the invention: the present invention provides a quantum key distribution method and system utilizing heterodyne measurement to realize four-state resolution. In the present invention, we introduce the key rate calculation method (Jie Lin, Twesh Upadhyaya, and Norbert Lütkenhaus, Asymptotic Security Analysis of Discrete-Modulated Continuous-Variable Quantum Key Distribution, Phys.Rev.X 9, 041064), and improved the discrete modulation quantum key distribution protocol proposed by it, breaking away from its use of signal light Strict limitation of the phase (requires that the central phase of the four signal lights and the central phase of the local oscillator light remain fixed

), and only by fixing the phase difference between the signal lights, the maximum resolution at the receiving end can be achieved. The phase difference between the signal light and the local oscillator light only affects the operation of data post-processing, but does not reduce the coding rate. After getting rid of the above limitations, the present invention reduces the difficulty of phase precision preparation, and at the same time does not need to continuously calculate phase compensation during the measurement process and act on the related equipment of the system, reducing the difficulty of phase feedback; on the other hand, our system sends There are few types of signal light and easy preparation, which simplifies the system, reduces the noise introduced by complex equipment, and can surpass the safe transmission distance and safe key rate of other continuous variable quantum key distribution systems, achieving simpler, safer, more efficient and Longer-distance key distribution.

Technical solution: In order to achieve the above object, the present invention proposes the following technical solutions:

A four-state quantum key distribution method based on heterodyne measurement, the method comprises the following steps:

；(1) The sending end prepares the local oscillator light and the original signal light, and then prepares the original signal light into one of the four signal lights with equal probability and randomly, and makes a difference between the degrees of freedom of the local oscillator light and signal light except for the phase amplitude Then combine the local oscillator light and the signal light and send them to the receiving end through the quantum channel; wherein, in each round of coding process, the four signal lights satisfy: take the phase of any one of the signal lights as the reference phase , the phase differences between the phases of the other three signal lights and the reference phase are 90°, 180°, and 270° respectively; the local oscillator light satisfies: a fixed phase difference is formed between the phase of the local oscillator light and the reference phase

;

(2) The sending end encodes the signal state corresponding to the signal light sent in each round of coding into a classic bit, and the classic bit is the initial key string of the sending end;

(3) The receiving end reunifies the degrees of freedom between the local oscillator light and the signal light except for the phase amplitude, takes the phase of the local oscillator light as the regular coordinate axis, and obtains the regular coordinate values of the signal light and the corresponding regular coordinates through heterodyne measurement. Momentum value, with the measured canonical coordinates as the real part and the canonical momentum as the imaginary part to form a complex result;

(4) The receiving end maps several complex number results obtained in one round of coding to the corresponding signal states of the four signal lights, and encodes the obtained signal states into the initial key string of the receiving end in the same way as the sending end;

(5) The sending end and the receiving end use the key rate calculation method based on convex optimization and dual problems to calculate the security key rate, and then perform classical error correction on the initial key string held by themselves and based on the calculated security key The rate of privacy amplification is obtained, and finally the security key is obtained.

For the above method, several optional methods are provided below, but they are not used as additional limitations on the above general scheme, but are only further additions or optimizations. On the premise of no technical or logical contradictions, each optional method can be used separately. Combinations of the above general schemes may also be a combination of multiple alternatives.

Optionally, in the step (3), the specific steps of mapping the complex result to a signal state include:

为一个相位角，以

为其余三个相位角，从复数坐标系原点引出对应所述四个相位角的四条射线；1) The phase of the local oscillator before heterodyne measurement is used as the 0 phase to construct a complex coordinate system, and the phase difference between the reference phase and the 0 phase

is a phase angle, with

For the remaining three phase angles, four rays corresponding to the four phase angles are drawn from the origin of the complex coordinate system;

2) Four fan-shaped areas are respectively formed with the four rays as the center, and each fan-shaped area corresponds to a signal state;

3) Each complex number result is mapped to the complex number coordinate system, and the signal state corresponding to each complex number result is obtained according to the fan-shaped area it falls into.

Optionally, the specific steps of calculating the security key rate by the key rate calculation method based on convex optimization and dual problem include:

Construct the key rate calculation model:

是使得量子的密度矩阵与经典比特有关联的映射，

表示收缩量子信道将

的映射结果投影到经典比特上，抛弃了不同经典比特结果关联；δ_EC代表着经典数据的比特纠错导致的比特损失，δ_EC＝(1-β)H(Z)-βH(Z|X)，其中β为纠错效率，H(Z)为Z的信息熵，H(Z|X)为在已知X情况下Z的信息熵；Pr_save表示保留某一个脉冲的数据用于生成密钥的概率。Among them, R ^∞ represents the key rate, ρ _AB represents the joint density matrix, S represents the constraint condition, H(ρ||σ) is the mutual entropy, which indicates the amount of information that is still unknown to the attacker after being attacked, through the convex optimization algorithm The lower bound of the minimum value obtained after solving;

is the mapping that associates the quantum density matrix with the classical bits,

Indicates that the contracted quantum channel will

The mapping result of is projected onto the classical bits, discarding the relationship between different classical bit results; δ _EC represents the bit loss caused by bit error correction of classical data, δ _EC =(1-β)H(Z)-βH(Z|X ), where β is the error correction efficiency, H(Z) is the information entropy of Z, H(Z|X) is the information entropy of Z when X is known; Pr _save means that the data of a certain pulse is reserved for generating encryption probability of the key.

The present invention also proposes a four-state quantum key distribution system based on heterodyne measurement, which is used to realize the method, and the system includes a sending end and a receiving end;

The sending end includes: a pulse light source module, an n:1 light splitting module, a signal local oscillator alienation module, a four-state preparation module, a combined output module and a sending end control module; wherein, the pulse light source module is used to prepare high-speed pulsed laser; n: 1. The optical splitting module prepares the high-speed pulsed laser into the original signal light and the local oscillator light; the signal local oscillator alienation module selects and modulates several degrees of freedom of the original signal light and the local oscillator light except the phase amplitude, so that the original signal light and the local oscillator light After being transmitted through the same optical path, it can be distinguished according to the several degrees of freedom; the four-state preparation module randomly prepares the original signal light into the four signal lights; the combined output module combines the four signal lights and the local oscillator light into Output to the receiving end after one pass; the control module of the sending end controls the remaining modules of the sending end to realize their respective functions, and conduct key negotiation with the control module of the receiving end;

The receiving end includes: a transmission calibration module, a signal local oscillator anti-alienation module, a heterodyne measurement four-state resolution module, and a receiving end control module; wherein, the transmission calibration module is used to receive the combined light and eliminate the combined light caused by the quantum channel transmission. parameter drift; the signal local oscillator anti-alienation module separates the signal light and local oscillator light, and restores the degree of freedom of the signal light and local oscillator light modulated by the signal local oscillator alienation module to the original state; heterodyne measurement four-state resolution The module measures the four kinds of signal light, and obtains the regular coordinates based on the phase of the local oscillation state and the corresponding regular momentum, and distinguishes the four signal states according to the regular coordinates and the regular momentum; the receiving end control module controls the other modules of the receiving end to realize their respective function, and perform key negotiation with the control module of the sending end.

For the above system, several optional methods are also provided below. On the premise of no technical or logical contradiction, each optional method can be combined for the above overall solution alone, or a combination of multiple optional methods can be used.

Optionally, the receiving end includes an electronic polarization controller connected through a polarization-maintaining optical fiber, first to third beam splitters, first to fourth detectors, first to second polarization-maintaining polarization beam splitters, the first One to the second differential amplifier; where,

The electronic polarization controller will receive the optical pulse sent by the sending end, and correct the polarization of the optical pulse, rotate the polarization corresponding to the local oscillator light to the fast axis of the fiber for transmission, and transmit the polarization corresponding to the signal light in the slow axis of the fiber transmission;

The first beam splitter divides the collimated light evenly into two beams and sends them to the first and second polarization maintaining beam splitters respectively;

第二分束器进行本振光与信号光干涉操作，将干涉后的两束光分别送至第一、第二探测器进行测量，第一、第二探测器的测量结果送至第一差分放大器进行差分放大，得到正则动量p；The first polarization-maintaining polarization beam splitter separates the signal light and local oscillator light components in the light beam according to local oscillator light reflection and signal light transmission, and rotates the polarization of the local oscillator light by 90° to keep the polarization of the local oscillator light and signal light consistent. Then the signal light and the local oscillator light are respectively transmitted to the second beam splitter through two sections of optical fiber with different lengths, so that the phase of the local oscillator light increases

The second beam splitter performs the interference operation between the local oscillator light and the signal light, and sends the two beams of light after interference to the first and second detectors for measurement, and the measurement results of the first and second detectors are sent to the first differential The amplifier performs differential amplification to obtain the regular momentum p;

The second polarization-maintaining polarization beam splitter separates the signal light and local oscillator light components in the light beam according to local oscillator light reflection and signal light transmission, and rotates the polarization of the local oscillator light by 90° to keep the polarization of the local oscillator light and signal light consistent. Then, the signal light and the local oscillator light are respectively transmitted to the third beam splitter through two sections of optical fibers with different lengths, so that the local oscillator light and the signal light enter the third beam splitter at the same time; the third beam splitter performs the local oscillator light and signal Optical interference operation, the two beams of light after interference are respectively sent to the third and fourth detectors for measurement, and the measurement results of the third and fourth detectors are sent to the second differential amplifier for differential amplification to obtain the regular coordinate q.

Optionally, the sending end includes a pulsed laser, an n:1 beam splitter, a phase modulator, and a polarization-maintaining polarization beam splitter connected through a polarization-maintaining optical fiber; wherein,

The pulsed laser sends pulses to the n:1 beam splitter through the polarization maintaining fiber;

n: 1 The beam splitter splits the pulse into original signal light and local oscillator light, sends the original signal light to the phase modulator, and sends the local oscillator light to the polarization-maintaining polarization beam splitter;

The phase modulator performs phase modulation on the original signal light to obtain the signal light corresponding to any one of the signal states, and then sends the signal light to the polarization-maintaining polarization beam splitter;

The signal light and the local oscillator light pass through different lengths of optical fibers from the beam splitter to the polarization-maintaining polarization beam splitter, so that the time when the signal light reaches the polarization-maintaining polarization beam splitter is between the current local oscillator light and the next local oscillator light. The middle of the time to arrive at the polarization-maintaining polarization beam splitter; the polarization-maintaining polarization beam splitter rotates the polarization of the phase-modulated signal light by 90° and then reflects it, directly transmits the local oscillator light, and finally sends the combined light to the sending end through a single-mode fiber .

Optionally, the sending end includes a master laser, a first slave laser, a second slave laser, a beam splitter, a first circulator, a second circulator, a fixed attenuator, a phase modulator, and a polarization maintaining polarization beam splitter ;in,

The master laser generates seed light and divides the seed light into two parts through the beam splitter, one part is injected into the first slave laser through the first circulator, and the other part is injected into the second slave laser through the second circulator;

The first slave laser generates the original signal light, and sends it to the fixed attenuator through the first circulator for attenuation, and the attenuated light beam is transmitted to the phase modulator for phase modulation to form signal light corresponding to any one of the signal states, The generated signal light is sent to the polarization maintaining polarization beam splitter;

The second slave laser generates local oscillator light, and sends the local oscillator light to the polarization-maintaining polarization beam splitter through the second circulator;

The polarization-maintaining polarization beam splitter combines the local oscillator light and the signal light and sends them to the receiving end through a single-mode fiber.

Optionally, the sending end includes a master laser, a first slave laser, a second slave laser, a beam splitter, a first circulator, a second circulator, a fixed attenuator, and a polarization-maintaining polarization beam splitter; wherein,

Under the input voltage, the master laser generates a beam of seed light every cycle and divides the seed light into two parts through the beam splitter. One part is injected into the first slave laser through the first circulator, and the other part is injected into the second laser through the second circulator. from the laser;

In the first half of each cycle, the second slave laser implements injection locking based on the seed light input by the master laser to generate local oscillator light, which is sent to the polarization-maintaining polarization beam splitter through the second circulator;

In the second half of each cycle, the first slave laser implements injection locking based on the seed light input by the master laser to generate signal light. The signal light is sent to the fixed attenuator through the first circulator for attenuation, and the attenuated signal light is sent to the Polarization maintaining polarization beam splitter;

The polarization-maintaining polarization beam splitter combines the local oscillator light and the signal light and sends them to the receiving end through a single-mode fiber.

Technical effect: Compared with the existing continuous variable quantum key distribution scheme, the present invention has the following advantages:

(1) The transmitting end of the present invention only needs to prepare four signal states with different phases, so it only needs to modulate the phase to encode, and no longer needs the combination of the amplitude modulation device and the phase modulation device to realize the encoding, so the equipment in the system Requirements are greatly reduced;

(2) The signal state only needs to meet the following conditions: take the phase of any one of the signal lights as the reference phase, and the phase differences between the phases of the remaining three signal lights and the reference phase are 90°, 180°, and 270° respectively. °; Therefore, there is no need to limit the phase relationship between the two signal lights before and after the preparation of the signal light, so you can get rid of the restriction that you must choose a continuous laser that maintains phase stability, and choose a continuous laser or a pulsed light source that has no front and rear phases Both are possible, and there is more freedom in the selection of the light source, and the present invention can also be normally implemented when faced with extreme conditions where a stable voltage cannot be provided.

即可，相位差

的取值没有特殊性，可以任意。因此信道中可以不引入根据相位反馈结果实时调整系统设备状态的操作，从而降低了信号与本振的制备难度以及相位反馈难度，进一步简化系统。(3) In the present invention, the local oscillator light only needs to ensure a fixed phase difference between the phase and the reference phase in the short period of one round of coding

Yes, the phase difference

The value of is not special and can be arbitrary. Therefore, the operation of adjusting the state of the system equipment in real time according to the phase feedback results may not be introduced in the channel, thereby reducing the difficulty of signal and local oscillator preparation and phase feedback, and further simplifying the system.

Description of drawings

Fig. 1 is the optical path diagram that system module of the present invention forms;

2 is a schematic diagram of the optical path structure of Embodiment 1 of the present invention;

FIG. 3 is a schematic diagram of the optical path structure of Embodiment 2 of the present invention;

FIG. 4 is a schematic diagram of an optical path structure in Embodiment 3 of the present invention.

Detailed ways

The invention provides a four-state quantum key distribution method, which reduces the phase dependence between the local oscillator light and the signal light, but does not reduce the coding rate, but reduces the difficulty of phase feedback, and the corresponding system can be more concise , so that the coding rate has increased.

The four-state quantum key distribution method is described as follows:

In the first step, the transmitting end prepares local oscillator light and four kinds of signal lights; the local oscillator light is considered as a classical strong light, and the signal light is a coherent light with a much smaller photon number than the classical strong light. The signal light prepared in this step satisfies the following conditions: taking the phase of one signal light as the reference phase, the phase differences between the phases of the other three signal lights and the reference phase are 90°, 180°, and 270°; and in this step The local oscillator light prepared in is satisfied: there is a fixed phase difference between the phase of the local oscillator light and the reference phase in a short time enough to form a round of coding, but the specific value can be arbitrary in different rounds, No control is required.

In the second step, the local oscillator light and the signal light are combined one by one, and then sent to the receiver for measurement through the quantum channel; Or some degrees of freedom can be distinguished, in this way, the photon leakage in transmission can be reduced, and it is convenient for the receiver to use separately.

In the third step, the receiving end reunifies the degrees of freedom between the local oscillator light and the signal light except for the phase amplitude, and uses the phase of the local oscillator light as the regular coordinate axis to obtain two measurement results by means of heterodyne measurement.

In the fourth step, after the data is generated, the receiving end estimates the phase in one round of coding to determine the corresponding relationship between the measurement result and the key and generate the key; then calculate the security key rate, classic error correction and privacy amplification ; Obtain the final security key.

The present invention also provides a four-state quantum key distribution system matched with the method, the system is composed of three parts: the sending end (Alice), the channel transmission part and the receiving end (Bob), these three parts are separated in space, There is a contextual relationship in time. The following is a more detailed description in conjunction with Figure 1:

The sending end includes a pulse light source module, an n:1 light splitting module, a signal local oscillator alienation module, a four-state preparation module and a combined output module. In addition, the control area that performs associated regulation on each module, performs post-processing on data, and performs classic communication with the receiving end is not directly reflected in the optical path diagram because it does not directly interact with the optical pulse.

The channel transmission part includes quantum channel and classical channel, depending on the spatial separation between the sending end and the receiving end, the quantum channel is realized by optical fiber, free space and other paths, and is used to transmit the output pulse prepared by the sending end to the receiving end in time , and the classical channel is used to transmit classical information.

The receiving end includes a transmission calibration module, a signal local oscillator anti-alienation module and a four-state resolution module for heterodyne measurement. In addition, the receiving end also has a control area for associated control of each module, post-processing of data, and classic communication with the sending end. To simplify the drawings, it is not directly reflected in the optical path diagram.

The functions to be realized by each module and the equipment to realize the corresponding functions are described below:

The function of the pulse light source module is to prepare a high-speed pulse laser with stable light intensity, fixed timing interval and extremely small, and stably input the slow axis of the polarization-maintaining fiber connected to the n:1 optical splitting module. It is particularly emphasized that the phases between the pulsed lights can be independent, and the realization of the system has nothing to do with the specific phase of the pulsed lights. Devices that can realize this function include, but are not limited to, internally modulated pulsed lasers and electroabsorption modulated pulsed lasers. Preferably, a fixed attenuator can be supplemented after the laser to remove stray light and improve the extinction ratio.

The function of the n:1 optical splitting module is to prepare the original signal light and the local oscillator light with the same phase at this moment and with multiple orders of magnitude difference in the number of photons. The equipment that can realize this function includes but is not limited to an n:1 beam splitter, It is also possible to use a combination of a polarizer that deflects the slow-axis light at a small angle into the fast axis and a polarization-maintaining polarization beam splitter, and finally realize the separation of two lights with the same phase and multiple orders of magnitude difference in the number of photons. prepared and output to two polarization-maintaining optical fibers respectively, wherein the light with a small number of photons is the signal light, and the light with a large number of photons is the local oscillator light. Preferably, a fixed attenuation can be inserted into the polarization-maintaining fiber through which the signal light passes, so as to further expand the photon number gap between the two beams of light to achieve the most favorable ratio for distribution.

The function of the signal local oscillator alienation module is to realize the distinguishability of signal light and local oscillator light after transmission in the same optical path. Furthermore, several degrees of freedom of the signal light and the local oscillator light except the phase amplitude are selected and modulated separately, so that the two have distinguishable characteristics in these degrees of freedom. Devices that can accomplish this include, but are not limited to, optical fibers of different lengths that can create time separations, polarization-maintaining polarization beam splitters that make polarizations orthogonal, and acousto-optic modulators that make small differences in frequency.

π、

的四种信号光。假设原始信号光与其对应本振光之间的相位差为

则制备好的四种信号光与其对应的本振光的相位差将为

可以在[0，2π)之间任意取值，不过因为我们制备的四个信号光相位差均为

的倍数，因此

每超过

都有一种信号光与本振光的相位差重新落入

因此本实施例中假定我们选择的基准信号光与本振光之间的相位差正向最小。另外，四种信号光和原始信号光的相位差也可以统一增加一个角度，不过这个角度可以等效于先让原始信号光与对应本振光多差出这样一个角度以后，再按照所述制备，即这个角度仍然归入

实现该功能的设备优选地只需要一个相位调制器，但不是唯一实现设备系统。特别地，以一个相位调制器作为该模块为例，该相位调制器可以放在被延长、信号态经过的光纤之间，从而在实现信号本振异化模块的功能时间分离的过程中，实现四种信号光的制备。Since the original signal light and local oscillator light output by the n:1 optical splitting module will change and drift in phase when they are transmitted in the optical fiber, after the signal local oscillator is dissimilated, the signal light needs to be randomly prepared by the four-state preparation module. The phase difference with the original signal light is 0,

π,

The four signal lights. Suppose the phase difference between the original signal light and its corresponding local oscillator light is

Then the phase difference between the prepared four kinds of signal light and the corresponding local oscillator light will be

It can take any value between [0, 2π), but because the phase differences of the four signal lights we prepared are

multiples of , so

every more than

There is a phase difference between the signal light and the local oscillator light falling into the

Therefore, in this embodiment, it is assumed that the phase difference between the reference signal light we choose and the local oscillator light is the smallest in the positive direction. In addition, the phase difference between the four signal lights and the original signal light can also be uniformly increased by an angle, but this angle can be equivalent to making the original signal light and the corresponding local oscillator light differ by such an angle, and then prepare according to the above, i.e. this angle still falls under the

A device implementing this function preferably requires only one phase modulator, but is not the only implementing device system. In particular, taking a phase modulator as an example of the module, the phase modulator can be placed between the optical fibers that are extended and the signal state passes through, so that in the process of realizing the functional time separation of the signal local oscillator alienation module, four Preparation of a signal light.

The function of the combined output module is to combine the signal light and the local oscillator light into one channel and stably input the quantum channel provided by the channel transmission part. Devices for this purpose include, but are not limited to, a polarization-maintaining polarization beam splitter. In particular, the device can not only meet the requirements of combining output modules to synthesize beams, but at the same time, the polarization-maintaining positive beam splitter rotates the polarization of the signal light by 90°, so that reflection occurs when passing through the device, while the local oscillator light is directly emitted from the device It is transmitted out, that is to say, the polarization of the signal light and the local oscillator light is orthogonalized, thereby realizing the functional requirements of the signal local oscillator alienation module.

The function of the transmission calibration module is to eliminate the parameter drift caused by the quantum channel transmission with a long optical path as completely as possible. The equipment to realize this function includes but is not limited to an electronic polarization controller, which recalibrates the polarization drift caused by the channel, and accurately inputs the light with orthogonal polarization into the slow axis and fast axis of the polarization-maintaining fiber respectively.

The function of the signal local oscillator anti-alienation module is the reverse operation of the signal local oscillator alienation module, and finally outputs two beams of signal light and local oscillator light respectively, which is to return the degrees of freedom of the signal light and local oscillator light except for the phase amplitude into same state. According to the selection of the signal local oscillator alienation module, different lengths of optical fibers will be selected to extend the optical fiber transmission channel of the short optical fiber, and the extended length is the same as the shortened length at the sending end; Beam splitter tuned back to the same and so on.

The function of the heterodyne measurement four-state resolution module is to efficiently and accurately distinguish four signal states with different phases. Devices that can be used include, but are not limited to, beam splitters, photodetectors, and differential amplifiers. The heterodyne measurement obtains the canonical coordinates based on the phase of the local oscillation state and the corresponding canonical momentum at the same time. The two results can be combined to construct four different situations, corresponding to the four signal states, so that the four can be efficiently and accurately distinguished. a signal state.

In addition, there is also a control area located at the sending end that associates and regulates each module of the sending end, performs post-processing on data, and performs classic communication with the receiving end. The control area needs to have the following capabilities: it cannot be accessed by attackers, and every The random number string of the sub-specifically prepared phase is used as the original key, and samples are randomly selected and the corresponding measurement results of the samples are obtained through classical communication. According to the measurement results, the unconditional security key rate is calculated by the security key rate calculation method integrating the convex optimization algorithm, and Combined receiver error correction and privacy amplification to extract the key.

The control area located at the receiving end that performs association regulation on each module of the receiving end, performs post-processing on the data, and performs classic communication with the sending end needs to have the following capabilities: cannot be accessed by attackers, and generates different phases corresponding to different numbers according to the measurement results The number string is used as the original key, and part of the measurement results are given through classical communication according to the request of the sender, and the key is extracted jointly with the sender for error correction and privacy amplification.

It should be noted that all the connecting lines in FIG. 1 do not represent the distance of optical paths between any actual systems. For any connection of the present invention to the optical path of the system embodied in the device, polarization-maintaining optical fibers are used in the sending end and the receiving end respectively. According to the specific requirements of each module and the polarization between modules, the specific connection method of the polarization-maintaining fiber will change, which has been described in the function of the module, and will be described in the embodiment if necessary. If there is no description, the slow axis of the polarization-maintaining fiber connected to the front and rear ends of the default device is aligned.

The present invention will be further described in detail below in conjunction with three embodiments.

Embodiment one:

Figure 2 shows an optical path diagram of a specific device connecting a sending end (Alice) and a receiving end (Bob) through an unsafe single-mode optical fiber. This embodiment provides an example of equipment and connection that requires the least equipment among the optical paths included in the system of the present invention. In this embodiment, Alice at the sending end includes an internally modulated pulsed laser, a beam splitter that can preferably be 999:1, a phase modulator, and a polarization-maintaining polarization beam splitter, and uses a polarization-maintaining fiber to connect them according to the optical path diagram connect.

Among them, the internally modulated pulse laser sends high-speed and stable pulses into the slow axis of the fiber through stable DC plus AC voltage to realize the function of the pulse light source module.

The beam splitter splits the pulse in the slow axis into signal light and local oscillator light, which are respectively input to the slow axis to realize the function of n:1 optical splitting module.

其中之一的相位旋转，并根据相位旋转分别记为{1，2，3，4}，并再次输入光纤慢轴，实现了四态制备模块的功能。The weak light from the beam splitting enters the phase modulator through the optical fiber as the signal light, and the phase modulator uniformly and randomly conducts the signal light

The phase rotation of one of them is recorded as {1, 2, 3, 4} according to the phase rotation, and input to the slow axis of the optical fiber again to realize the function of the four-state preparation module.

The signal light and the local oscillator light are generated from the beam splitter and then reach the polarization maintaining polarization beam splitter. This time the signal light reaches the polarization-maintaining polarization beam splitter later than the next local oscillator light, but it is in the middle of the time when the current local oscillation light and the next local oscillation light arrive at the polarization-maintaining polarization beam splitter; at the same time, using the polarization-maintaining polarization The beam splitter rotates the polarization of the signal light by 90° and reflects it, and transmits the local oscillator light directly. Therefore, not only the function of the signal local oscillator alienation module in the time degree of freedom and the polarization degree of freedom is realized, but also the function of the combined output module is completed.

Finally, the sending end inputs the combined beam into the single-mode optical fiber quantum channel.

The receiving end contains an electronic polarization controller, three beam splitters, two polarization maintaining polarization beam splitters, four detectors and two differential amplifiers, and they are connected according to the optical circuit diagram using polarization maintaining fibers.

The electronic polarization controller corrects the polarization of the light pulse passing through the single-mode fiber, so that it is aligned and input into the polarization-maintaining fiber. In particular, it means that the polarization corresponding to the local oscillator is rotated to the fast axis for transmission, and the corresponding signal light The corresponding polarization is transmitted in the slow axis of the optical fiber, thereby realizing the function required by the transmission calibration module.

使得本振光时间延后与信号光在相同时间窗口内进入第二分束器，且本振光额外增加了

的相位，用于测量正则动量p。在第二保偏偏振分束器到第三分束器之间的本振光，走过的光纤也比信号光长，长出部分为在Alice端比信号光短的光纤长度，使得本振光时间延后，从而与信号光同时进入第三分束器，但本振光不额外改变相位，用于测量正则坐标q。第二分束器和第三分束器分别进行本振光与信号光干涉操作，并通过相应的探测器和差分放大器输出测量结果，测量结果为两个实数，以正则坐标结果为实部、正则动量结果为虚部形成复数结果。以未旋转本振光的相位作为0相位(正实轴)，按照拥有基准相位的信号光与未旋转本振光之间的相位差

为一个相位角，以及

为相位角，从复数空间原点引出四条射线。相位差

包含了制备时的相位差

和在信道传输中引入的相位漂移。分别以这四条射线为中心，复数结果落在某射线增加或减少

的范围内的给予相同的密钥标记，以

为中心增加或减少

以内的记为1，以

为中心增加或减少

以内的记为2，以

为中心增加或减少

以内的记为3，以

为中心增加或减少

以内的记为4。优选地，估计

而带来的相位误差可以通过将不同密钥标记的分界线附近小范围内数据消除，从而降低错误率。优选地，为了进一步降低错误率，可以将落在原点周围半径为a的小区域中的测量结果不用于生成{1，2，3，4}的密钥串，只用于被随机抽取到时公布出来做参数估计和密钥率计算。半径a的具体取值应当通过密钥率计算的结果进行优化。可以看到，在实现外差测量四态分辨模块的同时，信号本振反异化模块的功能也一同实现了。The remaining equipment, three beam splitters, two polarization maintaining polarization beam splitters, four detectors and two differential amplifiers constitute a set of the simplest four-state resolution module for heterodyne measurement. Use the first beam splitter to split the light into two beams evenly to generate two outputs for heterodyne measurement. The first polarization-maintaining polarization beam splitter and the second polarization-maintaining polarization beam splitter separate the signal light in the two beams It is separated from the local oscillator light component according to local oscillator light reflection and signal light transmission, and the polarization of the local oscillator light is rotated by 90° to keep consistent with the signal light polarization. From the first polarization-maintaining polarization beam splitter to the second beam splitter, the optical fiber that the local oscillator light passes through is longer than the signal light, and the longer part is the length of the optical fiber that is shorter than the signal light at the Alice end. The short length allows the optical phase of the local oscillator to increase

The time delay of the local oscillator light and the signal light enter the second beam splitter in the same time window, and the local oscillator light additionally increases

The phase of is used to measure the canonical momentum p. The local oscillator light between the second polarization-maintaining polarization beam splitter and the third beam splitter also travels through an optical fiber longer than the signal light, and the longer part is the fiber length shorter than the signal light at the Alice end, so that the local The light time is delayed so that it enters the third beam splitter at the same time as the signal light, but the local oscillator light does not change the phase additionally, and is used to measure the canonical coordinate q. The second beam splitter and the third beam splitter respectively perform the interference operation of the local oscillator light and the signal light, and output the measurement results through the corresponding detectors and differential amplifiers. The measurement results are two real numbers, and the regular coordinate results are the real part, Regularized momentum results form complex results for the imaginary part. Taking the phase of the unrotated local oscillator light as 0 phase (positive real axis), according to the phase difference between the signal light with the reference phase and the unrotated local oscillator light

is a phase angle, and

is the phase angle, and four rays are drawn from the origin of the complex space. phase difference

Including the phase difference at the time of preparation

and the phase drift introduced in the channel transmission. Taking these four rays as the center respectively, the complex result falls on a certain ray to increase or decrease

range of given the same key tag to

increase or decrease centered

The ones within are recorded as 1, and the

increase or decrease centered

The ones within are recorded as 2, and the

increase or decrease centered

The ones within are recorded as 3, and the

increase or decrease centered

Those within are recorded as 4. Preferably, estimate

The resulting phase error can be eliminated by eliminating the data in a small range near the boundary of different key marks, thereby reducing the error rate. Preferably, in order to further reduce the error rate, the measurement results falling in a small area with a radius of a around the origin are not used to generate the key string of {1, 2, 3, 4}, but are only used to be randomly drawn when Publish it for parameter estimation and key rate calculation. The specific value of radius a should be optimized based on the result of key rate calculation. It can be seen that while realizing the four-state resolution module for heterodyne measurement, the function of the signal local oscillator anti-alienation module is also realized.

Through the above optical path, all module functions have been realized, and the required data has been collected. As long as the relevant functions of the control area described in the specific implementation are executed, the key distribution can be realized. The following describes in more detail how data is sequentially processed in the control area and key distribution is realized, so as to make the construction and use of the system of the present invention more complete.

Parameter estimation is first achieved by randomly disclosing partial data results. These parameters are then used to calculate the secure key rate and key error correction and privacy amplification. If the key rate calculation result is too small or even negative, discard this piece of data and restart from the pulse light source module. The mathematical description of the specific calculation method is as follows:

将相位旋转了

的四种信号光分别记为|μ₁>、|μ₂>、|μ₃>、|μ₄>，而将发送这四种信号光的事件分别记录为|1>、|2>、|3>、|4>，于是发送端相当于制备了一个纠缠态

其中的

部分被发送给接收端，

在信道里经过了一个完全正定且保迹的变换后变成B，于是得到整个系统光路部分的联合密度矩阵ρ_AB。由于信道传输部分可能存在攻击方，因此完全正定且保迹的变换具体形式未知，但是通过外差测量四态分辨模块的测量结果保证ρ_AB满足一些约束条件。这些约束条件记为S，包括但不限于：一、密度矩阵的性质，迹为1且半正定；二、完全正定且保迹的变换要求对ρ_AB中对B求偏迹与对ρ_AA′中A′求偏迹的结果一致；三、根据测量结果随机公布的部分得到对应测量算符作用在密度矩阵上的期望值(平均值)。满足这些约束条件的密度矩阵不唯一，不能够反推攻击者的具体攻击，但是密钥率公式与密度矩阵变量满足凸优化，可以根据凸优化算法寻找对攻击者最有利的结果，也就是密钥率下限。Denote the original signal light sent by the pulse light source module as

rotated the phase

The four kinds of signal lights are respectively recorded as |μ ₁ >, |μ ₂ >, |μ ₃ >, |μ ₄ >, and the events of sending these four kinds of signal lights are respectively recorded as |1>, |2>, | 3>, |4>, so the sender is equivalent to preparing an entangled state

one of them

part is sent to the receiver,

After a completely positive definite and trace-preserving transformation in the channel, it becomes B, so the joint density matrix ρ _AB of the optical path part of the entire system is obtained. Since there may be an attacker in the channel transmission part, the specific form of the fully positive definite and trace-preserving transformation is unknown, but the measurement results of the four-state resolution module through heterodyne measurement ensure that ρ _AB satisfies some constraints. These constraints _are denoted as S, including but not limited to: 1. The nature of the density matrix _, whose trace is 1 and positive semi-definite; In A', the result of calculating the deviation trace is consistent; 3. According to the randomly published part of the measurement results, the expected value (average value) of the corresponding measurement operator acting on the density matrix is obtained. The density matrix that satisfies these constraints is not unique and cannot reverse the specific attack of the attacker, but the key rate formula and the density matrix variables satisfy convex optimization, and the most beneficial result for the attacker can be found according to the convex optimization algorithm, that is, the secret Key rate lower limit.

The formula for the progressive key rate is R ^∞ = Pr _save (I(X; Z)-max _ρ∈S χ(Z: E)), where R ^∞ is the key rate, and Pr _save means to save the data of a pulse The probability of generating a key depends on the size of the area with a radius a deducted during optimization. I(X; Z) is the classic mutual information, where X refers to the key string at the sending end and Z refers to the key string at the receiving end, indicating that The amount of classical information with the same value in the corresponding position between the two; χ(Z:E) is Holevo information, which indicates the degree of understanding of Z by the attacker E, which means that what we want to use is the receiving end key string Z is the reverse coordination of the datum. ρ or ρ _AB is a density matrix that satisfies the constraints S mentioned above.

前一项H(ρ||σ)是相互熵，表明了被攻击后仍然不被攻击者知道的信息量，通过凸优化算法获得最小值的下限。其中的

是使得量子的密度矩阵与经典比特有关联的映射，

则是收缩量子信道将

的映射结果投影到经典比特上，抛弃了不同经典比特结果关联。后一项中δ_EC代表着经典数据的比特纠错导致的比特损失，δ_EC＝(1-β)H(Z)-βH(Z|X)，其中β为纠错效率，通常小于1，H(Z)为Z的信息熵，H(Z|X)为在已知X情况下Z的信息熵(即条件熵)。Phys.Rev.X 9,041064认为在约束S下求最小相互熵问题是一个数学上的凸优化问题，利用现有凸优化算法和对偶理论，求得最小值下限。Using information theory, this formula can be further rewritten as

The previous term H(ρ||σ) is mutual entropy, which indicates the amount of information that is still unknown to the attacker after being attacked, and the lower limit of the minimum value is obtained through the convex optimization algorithm. one of them

is the mapping that associates the quantum density matrix with the classical bits,

Then the shrinkage quantum channel will be

The mapping result of is projected onto the classical bits, and the result association of different classical bits is discarded. In the latter item, δ _EC represents the bit loss caused by bit error correction of classical data, δ _EC =(1-β)H(Z)-βH(Z|X), where β is the error correction efficiency, usually less than 1, H(Z) is the information entropy of Z, and H(Z|X) is the information entropy of Z when X is known (ie conditional entropy). Phys.Rev.X 9,041064 thinks that the problem of finding the minimum mutual entropy under the constraint S is a mathematical convex optimization problem. Using the existing convex optimization algorithm and dual theory, the lower limit of the minimum value is obtained.

Finally, when the key rate is greater than 0 by using the lower limit of the minimum value, the reverse coordination can be performed to perform classic error correction, error verification and privacy amplification, and finally extract the final key from the original key.

Embodiment two:

Fig. 3 shows another optical path diagram of a four-state quantum key distribution system based on heterodyne measurement. As shown in the figure, from the perspective of equipment and connection structure, the difference between this implementation and Figure 2 is only the sending end. In particular, the structure of the pulse light source module and the implementation order of the n:1 light splitting module are different from those shown in FIG. 2 .

There are three internally modulated pulsed lasers in the transmitting end, one of which is used as the master laser, and two slave lasers; one beam splitter, two circulators, one fixed attenuator, one phase modulator and one polarization-maintaining polarization beam splitter.

The master laser generates a seed light for injection into the slave laser, the first slave laser is used to generate signal light, and the second slave laser generates local oscillator light. The first circulator and the second circulator induce the seed light from the master laser to inject the first slave laser and the second slave laser respectively, and then respectively guide the light pulses generated by the first slave laser and the second slave laser into the fixed attenuator and the Different fibers directly connected to a PM polarization beam splitter. Note that the position of the beam splitter is placed at the output end of the main laser. The beam splitter still shoulders the function of separating the signal light and the local oscillator light, but what it actually separates is the seed light used to generate the signal light and the local oscillator light , thereby indirectly separating the signal light and the local oscillator light. Since the signal light generated from the first laser uses the principle of laser injection, the generated light intensity has almost nothing to do with the light intensity of the seed light, and the generated light intensity cannot be compared with the intensity of the local oscillator light. Therefore, it is necessary to place a A fixed attenuator is used to achieve an n:1 beam splitting effect. That is to say, the pulse light source module includes the signal light and local oscillator light generated by seed light and laser injection, but the generation of signal light and local oscillator light is realized by the functional device beam splitter belonging to the n:1 beam splitting module, so it shows Except for the alternate implementation of the pulse light source module and the n:1 beam splitter module, the two modules cannot be strictly distinguished in terms of device connection, but it is clear which module is used for each device.

，直接在相位反馈中处理，无需单独考虑。In addition, this method of injecting seed light into the slave laser to generate light pulses is called injection locking, which has a good phase locking function, that is, there is a stable phase relationship between the light generated from the slave laser and the injected light. This phase relationship can be calibrated in advance. Here, both the signal light and the local oscillator light maintain a stable phase relationship with the same original seed light, so a stable phase relationship is obtained between the two. This phase relationship drifts very little over time, and can be regarded as no change in a short period of time, so it is the unknown phase between the local oscillator light and the signal light described in the method

, are directly dealt with in the phase feedback and need not be considered separately.

Embodiment three:

With reference to FIG. 4 , this embodiment particularly provides a device optical path diagram in which a single device realizes the functional requirements of multiple modules. 4(a) in FIG. 4 of this embodiment shows the equipment and optical path diagram of the sending end, and the transmission channel and receiving end used by it are exactly the same as the corresponding parts in FIG. 3 , so it will not be given again here. 4(b) in FIG. 4 of this embodiment corresponds to the input voltage diagrams of the first slave laser, the master laser, and the second slave laser in 4(a) on the left from top to bottom. Note that these three voltage curves are aligned in time sequence, and the three voltage points that any vertical line passes through correspond to the voltage used by the master laser at this moment, and when the light generated by the master laser at this moment reaches the slave laser, the two slave lasers The voltage used by the laser respectively.

It can be seen from the figure that the main laser can be a continuous laser, which is fed with a stable DC voltage. The dotted line in the figure divides the illustrated time axis into four equidistant regions. In the first half of each time domain, the first Second, the voltage is applied to the slave laser, and the light input at the corresponding time with the master laser is injection-locked. The first half is used to generate local oscillator light; The input light corresponding to the time is implemented to achieve injection locking, and the second half is used to generate signal light.

给出。因此当变化时间δt给定时，只要通过控制电压波动的大小，就可以控制频率偏移Δv，进而可以控制产生的相位差，当我们用控制前后的光分别进行注入锁定时，就会在注入锁定带来的相位关系之外，额外为前后产生的光产生一个相位差

There is an additional feature in the voltage of the main laser. In the very short time δt in the middle of each time domain, the input voltage of the main laser has a small voltage fluctuation. As a continuous laser, the main laser has a stable center frequency when it is energized stably, and when the voltage changes, the center frequency will shift by Δv, which causes the phase to evolve according to the new center frequency within the change time, When the voltage returns to the initial stable value, the center frequency also returns to the original position, and the phase evolution resumes. However, the phase evolution in δt is different from the original evolution, resulting in a phase difference in the front and rear parts of the time domain. This phase difference can be calculated by

give. Therefore, when the change time δt is given, as long as the magnitude of the voltage fluctuation is controlled, the frequency offset Δv can be controlled, and then the generated phase difference can be controlled. In addition to the phase relationship brought about, an additional phase difference is generated for the light generated before and after

的相位差。种子光的相位差会通过注入锁定稳定地体现在本振光和信号光上，也就是说，通过随机选择四种电压波动，可以对应制备四种相位的信号态。这也就是图4中的4(a)相比于图3，在发送端缺少了一个相位调制器的原因。也就是说，这些激光器组同时实现了脉冲光源模块和四态制备模块的功能。同时，由于信号光和本振光的种子光在时间上分离，也实现了信号本振异化模块的功能。为此，必须要强调的是，信号光和本振光因为种子光在时间上分离而产生的时域分离，也需要在接收端的信号本振反异化模块得到补偿。不过补偿方法仅为延长或缩短原定的补偿光纤，没有增加设备或者改变连接方式，因此不再一次给出接收端的光路图，以示简洁。The four different voltage fluctuations in 4(b) in Figure 4 qualitatively indicate the relationship between the voltage to be used, and do not represent the actual voltage. The actual voltage fluctuation value used is calibrated for a specific laser. In the range of small voltage fluctuations, the magnitude of the fluctuating voltage signal has an approximately linear relationship with the phase deflection. Therefore, we can adjust the voltage fluctuation to realize the generation of the front and rear parts as seed light respectively.

phase difference. The phase difference of the seed light will be stably reflected in the local oscillator light and the signal light through injection locking, that is to say, by randomly selecting four kinds of voltage fluctuations, four phase signal states can be correspondingly prepared. This is why 4(a) in FIG. 4 lacks a phase modulator at the sending end compared to FIG. 3 . That is to say, these laser groups simultaneously realize the functions of the pulse light source module and the four-state preparation module. At the same time, since the signal light and the seed light of the local oscillator light are separated in time, the function of the signal local oscillator alienation module is also realized. For this reason, it must be emphasized that the time-domain separation of the signal light and the local oscillator light due to the temporal separation of the seed light also needs to be compensated by the signal local oscillator anti-alienation module at the receiving end. However, the compensation method is only to extend or shorten the original compensation fiber, without adding equipment or changing the connection mode, so the optical path diagram of the receiving end is not given again to show simplicity.

It should also be noted that the main laser does not have to be a continuous laser, because only the phase difference between the signal light and the corresponding local oscillator light affects the measurement results, so the main laser is replaced by an input voltage with a wider The platform, which can be divided into front and rear areas within one platform time, is a pulsed laser for preparing signal light and seed light of local oscillator light, and can also realize the above functions.

All the above-mentioned embodiments only express several specific implementations of the system of the present invention, and the descriptions thereof are relatively specific and detailed, but should not be construed as limiting the patent scope of the invention. It should be pointed out that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent for the present invention should be based on the appended claims.

Claims (7)

1. A four-state quantum key distribution method based on heterodyne measurement, characterized in that: the method comprises the following steps: (1) The sending end prepares the local oscillator light and the original signal light, and then prepares the original signal light into one of the four signal lights with equal probability and randomly, and makes a difference between the degrees of freedom of the local oscillator light and signal light except for the phase amplitude Then combine the local oscillator light and the signal light and send them to the receiving end through the quantum channel; wherein, in each round of coding process, the four signal lights satisfy: take the phase of any one of the signal lights as the reference phase , the phase differences between the phases of the other three signal lights and the reference phase are 90°, 180°, and 270° respectively; the local oscillator light satisfies: a fixed phase difference is formed between the phase of the local oscillator light and the reference phase

(2) The sending end encodes the signal state corresponding to the signal light sent in each round of coding into a classic bit, and the classic bit is the initial key string of the sending end; (3) The receiving end reunifies the degrees of freedom between the local oscillator light and the signal light except for the phase amplitude, takes the phase of the local oscillator light as the regular coordinate axis, and obtains the regular coordinate values of the signal light and the corresponding regular coordinates through heterodyne measurement. Momentum value, with the measured canonical coordinates as the real part and the canonical momentum as the imaginary part to form a complex result; (4) The receiving end maps several complex number results obtained in one round of coding to the corresponding signal states of the four signal lights, and encodes the obtained signal states into the initial key string of the receiving end in the same way as the sending end; (5) The sending end and the receiving end use the key rate calculation method based on convex optimization and dual problems to calculate the security key rate, and then perform classical error correction on the initial key string held by themselves and based on the calculated security key The rate of privacy amplification is obtained, and finally the security key is obtained; The steps for calculating the security key rate are: Construct and solve the key rate calculation model:

Among them, R ^∞ represents the key rate, ρ _AB represents the joint density matrix, S represents the constraint condition, H(ρ||σ) is the mutual entropy, which indicates the amount of information that is still unknown to the attacker after being attacked, through the convex optimization algorithm The lower bound of the minimum value obtained after solving;

is the mapping that associates the quantum density matrix with the classical bits,

Indicates that the contracted quantum channel will

The mapping result of is projected onto the classical bits; δ _EC represents the bit loss caused by bit error correction of classical data, δ _EC =(1-β)H(Z)-βH(Z|X), where β is the error correction efficiency , H(Z) is the information entropy of Z, H(Z|X) is the information entropy of Z when X is known; Pr _save indicates the probability of retaining a certain pulse of data for key generation. 2. a kind of four-state quantum key distribution method based on heterodyne measurement according to claim 1, is characterized in that: in described step (4), complex number result is mapped to the specific steps of signal state comprising: 1) The phase of the local oscillator before heterodyne measurement is used as the 0 phase to construct a complex coordinate system, and the phase difference between the reference phase and the 0 phase

is a phase angle, with

For the remaining three phase angles, four rays corresponding to the four phase angles are drawn from the origin of the complex coordinate system; 2) Four fan-shaped areas are respectively formed with the four rays as the center, and each fan-shaped area corresponds to a signal state; 3) Each complex number result is mapped to the complex number coordinate system, and the signal state corresponding to each complex number result is obtained according to the fan-shaped area it falls into. 3. A four-state quantum key distribution system based on heterodyne measurement, for realizing the method described in any one of claims 1 to 2, comprising a sending end and a receiving end, characterized in that: The sending end includes: a pulse light source module, n:1 splitting module, signal local oscillator alienation module, four-state preparation module, combined output module and sending end control module; wherein, the pulse light source module is used to prepare high-speed pulsed laser; n: 1. The optical splitting module prepares the high-speed pulsed laser into the original signal light and the local oscillator light; the signal local oscillator alienation module selects and modulates several degrees of freedom of the original signal light and the local oscillator light except the phase amplitude, so that the original signal light and the local oscillator light After being transmitted through the same optical path, it can be distinguished according to the several degrees of freedom; the four-state preparation module randomly prepares the original signal light into the four signal lights; the combined output module combines the four signal lights and the local oscillator light into Output to the receiving end after one pass; the control module of the sending end controls the remaining modules of the sending end to realize their respective functions, and conduct key negotiation with the control module of the receiving end; The receiving end includes: a transmission calibration module, a signal local oscillator anti-alienation module, a heterodyne measurement four-state resolution module, and a receiving end control module; wherein, the transmission calibration module is used to receive the combined light and eliminate the combined light caused by the quantum channel transmission. parameter drift; the signal local oscillator anti-alienation module separates the signal light and local oscillator light, and restores the degree of freedom of the signal light and local oscillator light modulated by the signal local oscillator alienation module to the original state; heterodyne measurement four-state resolution The module measures the four kinds of signal light, and obtains the regular coordinates based on the phase of the local oscillation state and the corresponding regular momentum, and distinguishes the four signal states according to the regular coordinates and the regular momentum; the receiving end control module controls the other modules of the receiving end to realize their respective function, and perform key negotiation with the control module of the sending end. 4. a kind of four-state quantum key distribution system based on heterodyne measurement according to claim 3, is characterized in that: The receiving end includes an electronic polarization controller connected by a polarization-maintaining optical fiber, first to third beam splitters, first to fourth detectors, first to second polarization-maintaining polarization beam splitters, first to second differential amplifier; where, The electronic polarization controller will receive the optical pulse sent by the sending end, and correct the polarization of the optical pulse, rotate the polarization corresponding to the local oscillator light to the fast axis of the fiber for transmission, and transmit the polarization corresponding to the signal light in the slow axis of the fiber transmission; The first beam splitter divides the collimated light evenly into two beams and sends them to the first and second polarization maintaining beam splitters respectively; The first polarization-maintaining polarization beam splitter separates the signal light and local oscillator light components in the light beam according to local oscillator light reflection and signal light transmission, and rotates the polarization of the local oscillator light by 90° to keep the polarization of the local oscillator light and signal light consistent. Then the signal light and the local oscillator light are respectively transmitted to the second beam splitter through two sections of optical fiber with different lengths, so that the phase of the local oscillator light increases

The second beam splitter performs the interference operation between the local oscillator light and the signal light, and sends the two beams of light after interference to the first and second detectors for measurement, and the measurement results of the first and second detectors are sent to the first differential The amplifier performs differential amplification to obtain the regular momentum p; The second polarization-maintaining polarization beam splitter separates the signal light and local oscillator light components in the light beam according to local oscillator light reflection and signal light transmission, and rotates the polarization of the local oscillator light by 90° to keep the polarization of the local oscillator light and signal light consistent. Then, the signal light and the local oscillator light are respectively transmitted to the third beam splitter through two sections of optical fibers with different lengths, so that the local oscillator light and the signal light enter the third beam splitter at the same time; the third beam splitter performs the local oscillator light and signal Optical interference operation, the two beams of light after interference are respectively sent to the third and fourth detectors for measurement, and the measurement results of the third and fourth detectors are sent to the second differential amplifier for differential amplification to obtain the regular coordinate q. 5. a kind of four-state quantum key distribution system based on heterodyne measurement according to claim 4, is characterized in that: The sending end includes a pulsed laser, an n:1 beam splitter, a phase modulator, and a polarization maintaining polarization beam splitter connected by a polarization-maintaining optical fiber; wherein, The pulsed laser sends pulses to the n:1 beam splitter through the polarization maintaining fiber; The n:1 beam splitter splits the pulse into original signal light and local oscillator light, sends the original signal light to the phase modulator, and sends the local oscillator light to the polarization-maintaining polarization beam splitter; The phase modulator performs phase modulation on the original signal light to obtain the signal light corresponding to any one of the signal states, and then sends the signal light to the polarization-maintaining polarization beam splitter; The signal light and the local oscillator light pass through different lengths of optical fibers from the beam splitter to the polarization-maintaining polarization beam splitter, so that the time when the signal light reaches the polarization-maintaining polarization beam splitter is between the current local oscillator light and the next local oscillator light. The middle of the time to arrive at the polarization-maintaining polarization beam splitter; the polarization-maintaining polarization beam splitter rotates the polarization of the phase-modulated signal light by 90° and then reflects it, directly transmits the local oscillator light, and finally sends the combined light to the sending end through a single-mode fiber . 6. a kind of four-state quantum key distribution system based on heterodyne measurement according to claim 4, is characterized in that: The sending end includes a master laser, a first slave laser, a second slave laser, a beam splitter, a first circulator, a second circulator, a fixed attenuator, a phase modulator, and a polarization-maintaining polarization beam splitter; wherein, The master laser generates seed light and divides the seed light into two parts through the beam splitter, one part is injected into the first slave laser through the first circulator, and the other part is injected into the second slave laser through the second circulator; The first slave laser generates the original signal light, and sends it to the fixed attenuator through the first circulator for attenuation, and the attenuated light beam is transmitted to the phase modulator for phase modulation to form signal light corresponding to any one of the signal states, The generated signal light is sent to the polarization maintaining polarization beam splitter; The second slave laser generates local oscillator light, and sends the local oscillator light to the polarization-maintaining polarization beam splitter through the second circulator; The polarization-maintaining polarization beam splitter combines the local oscillator light and the signal light and sends them to the receiving end through a single-mode fiber. 7. a kind of four-state quantum key distribution system based on heterodyne measurement according to claim 4, is characterized in that: The sending end includes a master laser, a first slave laser, a second slave laser, a beam splitter, a first circulator, a second circulator, a fixed attenuator, and a polarization-maintaining polarization beam splitter; wherein, Under the input voltage, the master laser generates a beam of seed light every cycle and divides the seed light into two parts through the beam splitter. One part is injected into the first slave laser through the first circulator, and the other part is injected into the second laser through the second circulator. from the laser; In the first half of each cycle, the second slave laser implements injection locking based on the seed light input by the master laser to generate local oscillator light, which is sent to the polarization-maintaining polarization beam splitter through the second circulator; In the second half of each cycle, the first slave laser implements injection locking based on the seed light input by the master laser to generate signal light. The signal light is sent to the fixed attenuator through the first circulator for attenuation, and the attenuated signal light is sent to the Polarization maintaining polarization beam splitter; The polarization-maintaining polarization beam splitter combines the local oscillator light and the signal light and sends them to the receiving end through a single-mode fiber.

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