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Quantum Communications and Quantum Networks

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Quantum Science and Technology".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 51906

Special Issue Editors

Dr. Davide Bacco

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Guest Editor
Department of Photonics Engineering, High-Speed Optical Communication Centre of Excellence for Silicon Photonics for Optical Communications, Technical University of Denmark, Ørsteds Plads, Building: 340, 1.13.E, 2800 Kgs. Lyngby, Denmark
Interests: quantum communications; high-dimensional quantum communications; quantum cryptography; silicon photonics for quantum communications
Dr. Guilherme B. Xavier

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Guest Editor
Department of Electrical Engineering, Linköping University, SE-581 83 Linköping, Sweden
Interests: experimental quantum communications; quantum key distribution; propagation of entanglement; optical fibers and associated optoelectronic instrumentation
Dr. Rui Lin

E-Mail Website
Guest Editor
Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
Interests: high-speed optical communication and network; digital signal processing; quantum key distribution; cyber security
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Quantum networks are the ultimate target in quantum communication, where many connected users can share information carried by quantum systems. The keystones of such structures are the reliable generation, transmission, and manipulation of quantum states. Two-dimensional quantum states, qubits, are steadily adopted as information units. However, high-dimensional quantum states, qudits, constitute a richer resource for future quantum networks, exceeding the limitations imposed by the ubiquitous qubits.

We are inviting you to submit to this Special Issue papers discussing quantum communication in its broadest sense. The scope of the Special Issue includes (among others) high-dimensional quantum communication, high-dimensional entanglement generation, teleportation, quantum cryptography, quantum error correction, and co-existence between quantum and classical light within the same channels.

Dr. Davide Bacco
Dr. Guilherme B. Xavier
Dr. Rui Lin
Guest Editors

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum communications
  • Quantum cryptography
  • High dimensional quantum communication
  • Co-existence quantum and classical signal

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Published Papers (16 papers)

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Research

15 pages, 3110 KiB  
Article
Quantum Key Distribution Networks: Challenges and Future Research Issues in Security
by Chia-Wei Tsai, Chun-Wei Yang, Jason Lin, Yao-Chung Chang and Ruay-Shiung Chang
Appl. Sci. 2021, 11(9), 3767; https://doi.org/10.3390/app11093767 - 22 Apr 2021
Cited by 29 | Viewed by 10407
Abstract
A quantum key distribution (QKD) network is proposed to allow QKD protocols to be the infrastructure of the Internet for distributing unconditional security keys instead of existing public-key cryptography based on computationally complex mathematical problems. Numerous countries and research institutes have invested enormous [...] Read more.
A quantum key distribution (QKD) network is proposed to allow QKD protocols to be the infrastructure of the Internet for distributing unconditional security keys instead of existing public-key cryptography based on computationally complex mathematical problems. Numerous countries and research institutes have invested enormous resources to execute correlation studies on QKD networks. Thus, in this study, we surveyed existing QKD network studies and practical field experiments to summarize the research results (e.g., type and architecture of QKD networks, key generating rate, maximum communication distance, and routing protocol). Furthermore, we highlight the three challenges and future research issues in the security of QKD networks and then provide some feasible resolution strategies for these challenges. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
►▼ Show Figures

Figure 1

Figure 1
<p>Framework of the quantum key distribution (QKD) network.</p> Full article ">Figure 2
<p>Schematic diagram of the quantum link.</p> Full article ">Figure 3
<p>Active optical switch network and trusted node network, in which (<b>a</b>) presents the schematic diagram of active optical switch based QKD network and (<b>b</b>) presents the schematic diagram of a trusted QKD network.</p> Full article ">Figure 4
<p>Schematic diagram of transmitting a session key, in which (<b>a</b>) presents the schematic diagram of transmitting session key in P2P method and (<b>b</b>) the schematic diagram of transmitting session key in point-to-multipoint (P2M) method.</p> Full article ">Figure 5
<p>Session key transmission method in the DARPA QKD network.</p> Full article ">Figure 6
<p>Session key transmission method in the SECOQC QKD network.</p> Full article ">Figure 7
<p>Session key transmission method using the multiple-path strategy.</p> Full article ">Figure 8
<p>Session key transmission method using quantum secret sharing (QSS).</p> Full article ">Figure 9
<p>Security interface between the quantum node and end users/applications.</p> Full article ">
18 pages, 867 KiB  
Article
A Scheme for Controlled Cyclic Asymmetric Remote State Preparation in Noisy Environment
by Nan Zhao, Tingting Wu, Yan Yu and Changxing Pei
Appl. Sci. 2021, 11(4), 1405; https://doi.org/10.3390/app11041405 - 4 Feb 2021
Cited by 4 | Viewed by 1756
Abstract
As research on quantum computers and quantum information transmission deepens, the multi-particle and multi-mode quantum information transmission has been attracting increasing attention. For scenarios where multi-parties transmit sequentially increasing qubits, we put forward a novel (N + 1)-party cyclic remote state preparation (RSP) [...] Read more.
As research on quantum computers and quantum information transmission deepens, the multi-particle and multi-mode quantum information transmission has been attracting increasing attention. For scenarios where multi-parties transmit sequentially increasing qubits, we put forward a novel (N + 1)-party cyclic remote state preparation (RSP) protocol among an arbitrary number of players and a controller. Specifically, we employ a four-party scheme in the case of a cyclic asymmetric remote state preparation scheme and demonstrate the feasibility of the scheme on the IBM Quantum Experience platform. Furthermore, we present a general quantum channel expression under different circulation directions based on the n-party. In addition, considering the impact of the actual environment in the scheme, we discuss the feasibility of the scheme affected by different noises. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
►▼ Show Figures

Figure 1

Figure 1
<p>The schematic of the four-party cyclic asymmetric remote state preparation (RSP) protocol. The black arrow points out the direction of the communications and the dashed line represents the control information.</p> Full article ">Figure 2
<p>The construction of the target channel. (<b>a</b>) Quantum circuit illustrating the construction of target channel. (<b>b</b>) The histogram shows theoretical and experimental results of the quantum state’s mean probability distribution. The x-axis of this histogram is arranged in the order of <math display="inline"><semantics> <mrow> <mo>(</mo> <msup> <mi>c</mi> <msup> <mrow/> <mrow> <mo>′</mo> <mo>′</mo> <mo>′</mo> </mrow> </msup> </msup> <mo>,</mo> <msup> <mi>b</mi> <msup> <mrow/> <mrow> <mo>′</mo> <mo>′</mo> </mrow> </msup> </msup> <mo>,</mo> <mo>⋯</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> from the bottom to the top, showing the average probability and percentage error of each state in the target channel of 13 qubits.</p> Full article ">Figure 3
<p>Diagram of four-party controlled cyclic asymmetrical RSP protocol, where SM is short for single-qubit measurement.</p> Full article ">Figure 4
<p>Quantum circuit illustrating four-party controlled cyclic asymmetrical RSP protocol.</p> Full article ">Figure 5
<p>Histogram of output results. (<b>a</b>) Histogram of output results after running once in the ’ibmq_qasm_simulator’ quantum processor. The x-axis of this histogram is arranged in the order of <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>8</mn> <mo>,</mo> <mo>⋯</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> from the bottom to the top. (<b>b</b>) Histogram of output results after running ten times in Jupyter Notebook. The x-axis of this histogram is arranged in the order of <math display="inline"><semantics> <mrow> <mo>(</mo> <msup> <mi>c</mi> <msup> <mrow/> <mrow> <mo>′</mo> <mo>′</mo> <mo>′</mo> </mrow> </msup> </msup> <mo>,</mo> <msup> <mi>b</mi> <msup> <mrow/> <mrow> <mo>′</mo> <mo>′</mo> </mrow> </msup> </msup> <mo>,</mo> <mo>⋯</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> from the bottom to the top.</p> Full article ">Figure 6
<p>The trend of the fidelity of the output state with the change of the decoherence rate(P) in four types of noisy environments, where different types of lines represent different noise environments. Suppose the coefficient of the desired state <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>The variations of the fidelity in different noise with different coefficients of the initiated state and decoherence rate, where P(D) is short for the decoherence rate of the depolarized noise, P(A) is short for the decoherence rate of the Amplitude damping noise, P(p) is short for the decoherence rate of the phase damping noise, P(S) is short for the decoherence rate of the bit-phase flip noise. Suppose the coefficient of the desired state is <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </mrow> </semantics></math>.</p> Full article ">
13 pages, 1625 KiB  
Article
Lengthening Transmission Distance of Continuous Variable Quantum Key Distribution with Discrete Modulation through Photon Catalyzing
by Zhengchun Zhou, Shanhua Zou, Tongcheng Huang and Ying Guo
Appl. Sci. 2020, 10(21), 7770; https://doi.org/10.3390/app10217770 - 3 Nov 2020
Viewed by 2107
Abstract
Establishing global secure networks is a potential implementation of continuous-variable quantum key distribution (CVQKD) but it is also challenged with respect to long-distance transmission. The discrete modulation (DM) can make up for the shortage of transmission distance in that it has a unique [...] Read more.
Establishing global secure networks is a potential implementation of continuous-variable quantum key distribution (CVQKD) but it is also challenged with respect to long-distance transmission. The discrete modulation (DM) can make up for the shortage of transmission distance in that it has a unique advantage against all side-channel attacks; however, its further performance improvement requires source preparation in the presence of noise and loss. Here, we consider the effects of photon catalysis (PC) on the DM-involved source preparation for improving the transmission distance. We address a zero-photon-catalysis (ZPC)-based source preparation for enhancing the DM–CVQKD system. The statistical fluctuation is taken into account for the practical security analysis. Numerical simulations show that the ZPC-based source preparation can not only achieve the long-distance transmission, but also contributes to the reasonable increase of the secret key rate. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
►▼ Show Figures

Figure 1

Figure 1
<p>The discrete-modulation (DM)-based sources for four states (<b>left</b>) and eight states (<b>right</b>).</p> Full article ">Figure 2
<p>The correlation comparison of <math display="inline"><semantics> <msub> <mi>Z</mi> <mn>4</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>Z</mi> <mn>8</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>Z</mi> <mi>G</mi> </msub> </semantics></math>.</p> Full article ">Figure 3
<p>Schematic diagram of continuous-variable quantum key distribution (CVQKD) with zero-photon-catalysis (ZPC)-based DM source preparation.</p> Full article ">Figure 4
<p>Success probabilities of ZPC with transmittances <math display="inline"><semantics> <mi>τ</mi> </semantics></math> and modulation variance <math display="inline"><semantics> <msub> <mi>V</mi> <mi>A</mi> </msub> </semantics></math>.</p> Full article ">Figure 5
<p>Asymptotic secret key rate of the CVQKD system with the ZPC-based DM source preparation for <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, where solid lines denote the eight-state DM source preparation, while dashed lines represent the four-state DM source preparation. The inserted subgraph shows that asymptotic secret key rate of the CVQKD system for <span class="html-italic">L</span> = 80 km.</p> Full article ">Figure 6
<p>(<b>a</b>) Asymptotic secret key rate of DM–CVQKD involving the ZPC operation for <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, where solid lines denote homodyne detection, while dashed lines heterodyne detection. (<b>b</b>) Corresponding to (<b>a</b>), the transmittance <math display="inline"><semantics> <mi>τ</mi> </semantics></math> varies with the transmission distance.</p> Full article ">Figure 7
<p>Finite-size key rate of CVQKD involving the ZPC operation for <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, where solid lines represent the eight-state DM source preparation and dotted lines represent the four-state DM source preparation, respectively.</p> Full article ">Figure 8
<p>Finite-size key rate of CVQKD involving the ZPC operation for <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, where the (<b>a</b>) represents eight-state DM source preparation, and inset (<b>b</b>) represents four-state DM source preparation.</p> Full article ">Figure 9
<p>The maximal tolerable excess noise of CVQKD involving the ZPC operation (dotted lines and solid lines) for the traditional CVQKD (dotted lines) and the ZPC-based CVQKD (solid lines), where (<b>a</b>) represents eight-state DM source preparation, and inset (<b>b</b>) represents four-state DM source preparation.</p> Full article ">Figure 10
<p>The secret key rate of the CVQKD system involving the ZPC operation with <span class="html-italic">L</span> = 50 km and <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math> for the traditional CVQKD system (dotted lines) and the ZPC-based CVQKD system (solid lines), where (<b>a</b>) represents eight-state DM source preparation, and inset (<b>b</b>) represents four-state DM source preparation.</p> Full article ">
18 pages, 937 KiB  
Article
Quantum Proxy Signature Scheme with Discrete Time Quantum Walks and Quantum One-Time Pad CNOT Operation
by Yanyan Feng, Qian Zhang, Jinjing Shi, Shuhui Chen and Ronghua Shi
Appl. Sci. 2020, 10(17), 5770; https://doi.org/10.3390/app10175770 - 20 Aug 2020
Cited by 6 | Viewed by 2934
Abstract
The quantum proxy signature is one of the most significant formalisms in quantum signatures. We put forward a quantum proxy signature scheme using quantum walk-based teleportation and quantum one-time pad CNOT (QOTP-CNOT) operation, which includes four phases, i.e., initializing phase, authorizing phase, signing [...] Read more.
The quantum proxy signature is one of the most significant formalisms in quantum signatures. We put forward a quantum proxy signature scheme using quantum walk-based teleportation and quantum one-time pad CNOT (QOTP-CNOT) operation, which includes four phases, i.e., initializing phase, authorizing phase, signing phase and verifying phase. The QOTP-CNOT is achieved by attaching the CNOT operation upon the QOTP and it is applied to produce the proxy signature state. The quantum walk-based teleportation is employed to transfer the encrypted message copy derived from the binary random sequence from the proxy signer to the verifier, in which the required entangled states do not need to be prepared ahead and they can be automatically generated during quantum walks. Security analysis demonstrates that the presented proxy signature scheme has impossibility of denial from the proxy and original signers, impossibility of forgery from the original signatory and the verifier, and impossibility of repudiation from the verifier. Notably, the discussion shows the complexity of the presented algorithm and that the scheme can be applied in many real scenarios, such as electronic payment and electronic commerce. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
►▼ Show Figures

Figure 1

Figure 1
<p>Shift rules of quantum walks on a circle with <span class="html-italic">P</span> vertices.</p> Full article ">Figure 2
<p>Schematic of the designed quantum proxy signature scheme. Charlie, Alice, Bob, and Trent are the original signer, the proxy signer, the verifier and the arbitrator, respectively. Notably, blue dashed box represents the initializing phase and authorizing phase, and green represents the signing phase and orange represents the verifying phase.</p> Full article ">Figure 3
<p>Alice packages <math display="inline"><semantics> <msub> <mrow> <mo>|</mo> <mi>φ</mi> <mo>〉</mo> </mrow> <msup> <mi>M</mi> <mo>′</mo> </msup> </msub> </semantics></math> with unitary operation <span class="html-italic">U</span> governed by the random sequence <span class="html-italic">S</span> to obtain <math display="inline"><semantics> <msub> <mrow> <mo>|</mo> <mi>φ</mi> <mo>〉</mo> </mrow> <msup> <mi>M</mi> <mrow> <mo>″</mo> </mrow> </msup> </msub> </semantics></math>.</p> Full article ">Figure 4
<p>The encryption process of <math display="inline"><semantics> <msub> <mrow> <mo>|</mo> <mi>φ</mi> <mo>〉</mo> </mrow> <msup> <mi>M</mi> <mrow> <mo>″</mo> </mrow> </msup> </msub> </semantics></math> based on <math display="inline"><semantics> <msub> <mi>K</mi> <mrow> <mi>A</mi> <mi>T</mi> </mrow> </msub> </semantics></math>. (<b>a</b>) Quantum circuit for the encryption process of <math display="inline"><semantics> <msub> <mrow> <mo>|</mo> <mi>φ</mi> <mo>〉</mo> </mrow> <msup> <mi>M</mi> <mrow> <mo>″</mo> </mrow> </msup> </msub> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math> including <span class="html-italic">X</span>, <span class="html-italic">Z</span> and CNOT gates governed by <math display="inline"><semantics> <msub> <mi>K</mi> <mrow> <mi>A</mi> <mi>T</mi> </mrow> </msub> </semantics></math> and ID refers to the identity gate; (<b>b</b>) The probability producing the encrypted quantum state <math display="inline"><semantics> <mrow> <mo>|</mo> <msub> <mi>S</mi> <mi>A</mi> </msub> <mo>〉</mo> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>The decryption process for recreating <math display="inline"><semantics> <msub> <mrow> <mo>|</mo> <mi>φ</mi> <mo>〉</mo> </mrow> <msup> <mi>M</mi> <mrow> <mo>″</mo> </mrow> </msup> </msub> </semantics></math> based on <math display="inline"><semantics> <msub> <mi>K</mi> <mrow> <mi>A</mi> <mi>T</mi> </mrow> </msub> </semantics></math>. (<b>a</b>) Quantum circuit for the encryption and decryption processes for obtaining <math display="inline"><semantics> <msub> <mrow> <mo>|</mo> <mi>φ</mi> <mo>〉</mo> </mrow> <msup> <mi>M</mi> <mrow> <mo>″</mo> </mrow> </msup> </msub> </semantics></math>. It can be seen that the gates for encryption and decryption processes are symmetric; (<b>b</b>) The probability recovering the quantum state <math display="inline"><semantics> <msub> <mrow> <mo>|</mo> <mi>φ</mi> <mo>〉</mo> </mrow> <msup> <mi>M</mi> <mrow> <mo>″</mo> </mrow> </msup> </msub> </semantics></math>.</p> Full article ">Figure 6
<p>Successful probability <math display="inline"><semantics> <msub> <mi>P</mi> <mi>n</mi> </msub> </semantics></math> for forging the random binary sequence <span class="html-italic">S</span> as a function of the length <span class="html-italic">n</span> of the sequence <span class="html-italic">S</span>.</p> Full article ">Figure 7
<p>Application scene of our presented proxy signature scheme in electronic payment.</p> Full article ">
12 pages, 1593 KiB  
Article
Monte Carlo-Based Performance Analysis for Underwater Continuous-Variable Quantum Key Distribution
by Yiyu Mao, Xuelin Wu, Wenti Huang, Qin Liao, Han Deng, Yijun Wang and Ying Guo
Appl. Sci. 2020, 10(17), 5744; https://doi.org/10.3390/app10175744 - 19 Aug 2020
Cited by 15 | Viewed by 2460
Abstract
There is a growing interest in the security of underwater communication with the increasing demand for undersea exploration. In view of the complex composition and special optical properties of seawater, this paper deals with a performance analysis for continuous-variable quantum key distribution (CVQKD) [...] Read more.
There is a growing interest in the security of underwater communication with the increasing demand for undersea exploration. In view of the complex composition and special optical properties of seawater, this paper deals with a performance analysis for continuous-variable quantum key distribution (CVQKD) over an underwater link. In particular, we focus on analyzing the channel transmittance and detection efficiency based on Monte Carlo simulation for different water types, link distances and transceiver parameters. A comparison between the transmittance obtained by simple Beer’s law and Monte Carlo simulation reveals that the transmittance of underwater link may be severely underestimated in the previous underwater CVQKD research. The effect of the receiver aperture and field of view (FOV) on detection efficiency under different water types is further evaluated based on Monte Carlo. Simulation results show that the transmission distance of the underwater CVQKD system obtained by Monte Carlo simulation in pure sea water, clear ocean water and coastal ocean water is larger than that obtained by Beer’s law, while the key rate of the system in all types of water is smaller than that obtained by Beer’s law because the size and FOV of the receiver aperture are taken into account. By considering the practical system parameters, this paper establishes a comprehensive model for evaluating the security of underwater CVQKD systems with different system configurations. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
►▼ Show Figures

Figure 1

Figure 1
<p>Schematic diagram of an underwater CVQKD system. The sender Alice separates coherent light pulses generated by a laser diode into weak signal pulses and strong LO pulses. Then the signal pulses are loaded with key information by using an amplitude modulator and a phase modulator, and the LO pulses are delayed by a delay line so as to be transmitted together with the signal pulses through time multiplexing. After being transmitted through the seawater, the pulses reach Bob’s telescope. Bob first separates the LO and signal pulses by using a beam splitter, and then randomly measures one of the quadratures of the signal states by homodyne detection, with the help of the LO as a phase reference. The phase modulator in Bob is used to randomly select the quadrature by imposing a <math display="inline"><semantics> <mrow> <mi>π</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> phase shift to the LO. The dark spots between Alice and Bob indicate the water components such as phytoplankton, suspended sediments and detritus, and colored dissolved organic matter. AM: amplitude modulator. PM: phase modulator. Tele.: telescope. BS: beam splitter. PD: photodiode. LO: local oscillator.</p> Full article ">Figure 2
<p>Transmittance of four types of water obtained by Beer’s law and Monte Carlo simulation. The solid lines correspond to the transmittance obtained by Monte Carlo simulation, and the dashed lines correspond to the transmittance obtained by Beer’s law. From left to right, the lines correspond, respectively, to turbid harbor water, coastal ocean water, clear ocean water, and pure sea water case. MC: results obtained by Monte Carlo simulation. BL: results calculated by Beer’s law.</p> Full article ">Figure 3
<p>Schematic diagram showing the geometry of the transceiver and the moving trajectory of photons in seawater. <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mi>y</mi> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mi>z</mi> </msub> </mrow> </semantics></math> are the angles between the direction vector of the photon and the x, y, and z-axis, respectively. <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math> represents the maximum initial divergence angle of the beam and FOV represents the field of view of the receiver.</p> Full article ">Figure 4
<p>(<b>a</b>) <math display="inline"><semantics> <msub> <mi>η</mi> <mi>r</mi> </msub> </semantics></math> calculated by Monte Carlo simulation versus different size of receiver aperture under four types of water. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>η</mi> <mi>r</mi> </msub> </semantics></math> calculated by Monte Carlo simulation versus different receiver FOV under four types of water.</p> Full article ">Figure 5
<p>Intensity distributions of the light with a beam width of (<b>a</b>) 1 mm, (<b>b</b>) 2 mm, (<b>c</b>) 3 mm at the reception plane after transmitting through a 10 m clear ocean water. Intensity distributions of the light with a maximum beam divergence angle of (<b>d</b>) 0 mrad, (<b>e</b>) 2 mrad, (<b>f</b>) 5 mrad at the reception plane after transmitting through a 10 m clear ocean water.</p> Full article ">Figure 6
<p>(<b>a</b>) Secret key rate of four types of water obtained by Beer’s law and Monte Carlo simulation. The solid lines correspond to the results obtained by Monte Carlo with considering the receiver parameters, the dashed lines correspond to the results obtained by Beer’s law, and the dot-dashed lines correspond to the results obtained by Monte Carlo without considering the receiver parameters. From left to right, the curves correspond, respectively, to the turbid harbor water case, the coastal ocean water case, the clear ocean water case and the pure see water case. (<b>b</b>) Secret key rate for different beam width <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>0</mn> </msub> </semantics></math> and maximum initial divergence angle <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math>.</p> Full article ">
13 pages, 2162 KiB  
Article
Bidirectional Quantum Communication through the Composite GHZ-GHZ Channel
by Shuangshuang Shuai, Na Chen and Bin Yan
Appl. Sci. 2020, 10(16), 5500; https://doi.org/10.3390/app10165500 - 8 Aug 2020
Cited by 2 | Viewed by 2750
Abstract
This paper solved the problem of transmitting quantum bits (qubits) in a multi-hop and bidirectional way. Considering that the Greenberger–Horne–Zeilinger (GHZ) states are less prone to the decoherence effects caused by the surrounding environment, we proposed a bidirectional quantum communication scheme based on [...] Read more.
This paper solved the problem of transmitting quantum bits (qubits) in a multi-hop and bidirectional way. Considering that the Greenberger–Horne–Zeilinger (GHZ) states are less prone to the decoherence effects caused by the surrounding environment, we proposed a bidirectional quantum communication scheme based on quantum teleportation and the composite GHZ-GHZ states. On a multi-hop quantum path, different types of GHZ states are previously shared between the adjacent intermediate nodes. To implement qubit transmission, the sender and intermediate nodes perform quantum measurements in parallel, and then send their measurement results and the types of previously shared GHZ states to the receiver independently. Based on the received information, the receiver performs unitary operations on the local particle, thus retrieving the original qubit. Our scheme can avoid information leakage at the intermediate nodes and can reduce the end-to-end communication delay, in contrast to the hop-by-hop qubit transmission scheme. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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<p>The composite Greenberger–Horne–Zeilinger (GHZ)-GHZ state previously shared between Alice and Bob.</p> Full article ">Figure 2
<p>Quantum circuit for one-hop bidirectional quantum communication, where the dashed lines represent classical channels and the solid lines represent quantum channels.</p> Full article ">Figure 3
<p>The composite GHZ-GHZ entanglement channel in a two-hop quantum communication case.</p> Full article ">Figure 4
<p>Quantum circuit for two-hop bidirectional quantum communication.</p> Full article ">Figure 5
<p>The composite GHZ-GHZ entanglement channel in the <span class="html-italic">n</span>-hop quantum communication case.</p> Full article ">Figure 6
<p>An example of multi-hop bidirectional quantum communication.</p> Full article ">Figure 7
<p>The proposed scheme in this paper.</p> Full article ">Figure 8
<p>Hop-by-hop qubit transmission.</p> Full article ">Figure 9
<p>The comparison of two schemes in terms of communication delay.</p> Full article ">
15 pages, 1745 KiB  
Article
Photon Subtraction-Induced Plug-and-Play Scheme for Enhancing Continuous-Variable Quantum Key Distribution with Discrete Modulation
by Chao Yu, Shanhua Zou, Yun Mao and Ying Guo
Appl. Sci. 2020, 10(12), 4175; https://doi.org/10.3390/app10124175 - 17 Jun 2020
Cited by 2 | Viewed by 2257
Abstract
Establishing high-rate secure communications is a potential application of continuous-variable quantum key distribution (CVQKD) but still challenging for the long-distance transmission technology compatible with modern optical communication systems. Here, we propose a photon subtraction-induced plug-and-play scheme for enhancing CVQKD with discrete-modulation (DM), avoiding [...] Read more.
Establishing high-rate secure communications is a potential application of continuous-variable quantum key distribution (CVQKD) but still challenging for the long-distance transmission technology compatible with modern optical communication systems. Here, we propose a photon subtraction-induced plug-and-play scheme for enhancing CVQKD with discrete-modulation (DM), avoiding the traditional loopholes opened by the transmission of local oscillator. A photon subtraction operation is involved in the plug-and-play scheme for detection while resisting the extra untrusted source noise of the DM-CVQKD system. We analyze the relationship between secret key rate, channel losses, and untrusted source noise. The simulation result shows that the photon-subtracted scheme enhances the performance in terms of the maximal transmission distance and make up for the deficiency of the original system effectively. Furthermore, we demonstrate the influence of finite-size effect on the secret key rate which is close to the practical implementation. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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<p>Phase space representations of coherent states with (<b>a</b>) four-state modulation and (<b>b</b>) eight-state modulation.</p> Full article ">Figure 2
<p>(<b>a</b>) the EB scheme of PP DM-CVQKD protocol. Here, Fred is assumed to controlled by Eve, and he will introduce an untrusted source noise; (<b>b</b>) the corresponding PS-based PP DM-CVQKD scheme. PNRD, photon number resolving detector.</p> Full article ">Figure 3
<p>The success probability of photon subtraction as a function of transmittance <math display="inline"><semantics> <mi>μ</mi> </semantics></math> for the modulation variance <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>The secret key rate as a function of channel losses. The solid line corresponds to the case that <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and the dash line corresponds to <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>1.005</mn> </mrow> </semantics></math>. The modulation variance <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, the channel excess noise <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, and the reconciliation efficiency <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>The secret key rate of plug-and-play DM-CVQKD of (<b>a</b>) PP 4-state DM-CVQKD protocol, (<b>b</b>) PP 8-state DM-CVQKD protocol, (<b>c</b>) 1-PS PP 4-state DM-CVQKD protocol and (<b>d</b>) 2-PS PP 4-state DM-CVQKD protocol. The modulation variance <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, the channel excess noise <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, and the reconciliation effiency <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>.</p> Full article ">Figure 6
<p>The secret key rate as a function of channel losses for PP DM-CVQKD protocol in the finite-size scenario. (<b>a</b>) PP four-state protocol; (<b>b</b>) PP eight-state protocol; (<b>c</b>) 1-PS PP four-state protocol; (<b>d</b>) 2-PS PP four-state protocol. The parameters are as follows: the modulation variance <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, the channel excess noise <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, the reconciliation efficiency <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math> and the gain <span class="html-italic">g</span> = 1.005.</p> Full article ">Figure 6 Cont.
<p>The secret key rate as a function of channel losses for PP DM-CVQKD protocol in the finite-size scenario. (<b>a</b>) PP four-state protocol; (<b>b</b>) PP eight-state protocol; (<b>c</b>) 1-PS PP four-state protocol; (<b>d</b>) 2-PS PP four-state protocol. The parameters are as follows: the modulation variance <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, the channel excess noise <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, the reconciliation efficiency <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math> and the gain <span class="html-italic">g</span> = 1.005.</p> Full article ">
11 pages, 438 KiB  
Article
Generation and Distribution of Quantum Oblivious Keys for Secure Multiparty Computation
by Mariano Lemus, Mariana F. Ramos, Preeti Yadav, Nuno A. Silva, Nelson J. Muga, André Souto, Nikola Paunković, Paulo Mateus and Armando N. Pinto
Appl. Sci. 2020, 10(12), 4080; https://doi.org/10.3390/app10124080 - 12 Jun 2020
Cited by 10 | Viewed by 5366
Abstract
The oblivious transfer primitive is sufficient to implement secure multiparty computation. However, secure multiparty computation based on public-key cryptography is limited by the security and efficiency of the oblivious transfer implementation. We present a method to generate and distribute oblivious keys by exchanging [...] Read more.
The oblivious transfer primitive is sufficient to implement secure multiparty computation. However, secure multiparty computation based on public-key cryptography is limited by the security and efficiency of the oblivious transfer implementation. We present a method to generate and distribute oblivious keys by exchanging qubits and by performing commitments using classical hash functions. With the presented hybrid approach of quantum and classical, we obtain a practical and high-speed oblivious transfer protocol. We analyse the security and efficiency features of the technique and conclude that it presents advantages in both areas when compared to public-key based techniques. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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<p>In secure multiparty computation, N parties compute a function preserving the privacy of their own input. Each party only has access to their own input–output pair.</p> Full article ">Figure 2
<p>Quantum OT protocol based on secure commitments. The ⨁ denotes the bit XOR of all the elements in the family.</p> Full article ">Figure 3
<p>Oblivious keys. Alice has the string <span class="html-italic">k</span> and Bob the string <math display="inline"><semantics> <mover accent="true"> <mi>k</mi> <mo>˜</mo> </mover> </semantics></math>. For each party, the boxes in the left and right represent the bits of their string associated to the indices <span class="html-italic">i</span> for which <math display="inline"><semantics> <msub> <mi>x</mi> <mi>i</mi> </msub> </semantics></math> equals 0 (<b>left box</b>) or 1 (<b>right box</b>). Alice knows the entire key, Bob only knows half of the key, but Alice does not know which half Bob knows.</p> Full article ">Figure 4
<p>Commitment protocol based on collision resistant hash functions.</p> Full article ">
12 pages, 1389 KiB  
Article
Improving Continuous Variable Quantum Secret Sharing with Weak Coherent States
by Yijun Wang, Bing Jia, Yun Mao, Xuelin Wu and Ying Guo
Appl. Sci. 2020, 10(7), 2411; https://doi.org/10.3390/app10072411 - 1 Apr 2020
Cited by 2 | Viewed by 2209
Abstract
Quantum secret sharing (QSS) can usually realize unconditional security with entanglement of quantum systems. While the usual security proof has been established in theoretics, how to defend against the tolerable channel loss in practices is still a challenge. The traditional ( [...] Read more.
Quantum secret sharing (QSS) can usually realize unconditional security with entanglement of quantum systems. While the usual security proof has been established in theoretics, how to defend against the tolerable channel loss in practices is still a challenge. The traditional ( t , n ) threshold schemes are equipped in situation where all participants have equal ability to handle the secret. Here we propose an improved ( t , n ) threshold continuous variable (CV) QSS scheme using weak coherent states transmitting in a chaining channel. In this scheme, one participant prepares for a Gaussian-modulated coherent state (GMCS) transmitted to other participants subsequently. The remaining participants insert independent GMCS prepared locally into the circulating optical modes. The dealer measures the phase and the amplitude quadratures by using double homodyne detectors, and distributes the secret to all participants respectively. Special t out of n participants could recover the original secret using the Lagrange interpolation and their encoded random numbers. Security analysis shows that it could satisfy the secret sharing constraint which requires the legal participants to recover message in a large group. This scheme is more robust against background noise due to the employment of double homodyne detection, which relies on standard apparatuses, such as amplitude and phase modulators, in favor of its potential practical implementations. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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<p>The state preparation of participants and the dealer. L is laser, M represents modulator, BS is beam splitter, DHD expresses double homodyne detector, and <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>}</mo> </mrow> </semantics></math> are independent Gaussian random numbers retained by the <math display="inline"><semantics> <msup> <mi>j</mi> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </semantics></math> participant <math display="inline"><semantics> <msub> <mi>B</mi> <mi>j</mi> </msub> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>j</mi> <mo>∈</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>n</mi> <mo>}</mo> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>The data-processing of legitimate <span class="html-italic">t</span> participants and the dealer. L is laser, M represents modulator, BS is beam splitter, DHD expresses double homodyne detector, <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>}</mo> </mrow> </semantics></math> are independent Gaussian random numbers retained by participant <math display="inline"><semantics> <mrow> <msub> <mi>B</mi> <mi>j</mi> </msub> <mo>,</mo> <mrow> <mo>{</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>,</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>l</mi> <msub> <mi>j</mi> <mi>l</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>}</mo> </mrow> </mrow> </semantics></math> is the private key of <math display="inline"><semantics> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>j</mi> </mrow> </msub> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>∈</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>t</mi> <mo>}</mo> <mo>,</mo> <mi>j</mi> <mo>∈</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>n</mi> <mo>}</mo> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>The secure rates of different kinds distribution of legitimate participants for <math display="inline"><semantics> <mrow> <msubsup> <mi>ρ</mi> <mrow> <mi>l</mi> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow> <mo>−</mo> <mn>0.2</mn> <mi>l</mi> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>ρ</mi> <mrow> <mi>l</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mfrac> <mi>l</mi> <mi>t</mi> </mfrac> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>ρ</mi> <mrow> <mi>l</mi> </mrow> <mn>3</mn> </msubsup> <mo>=</mo> <msqrt> <mfrac> <mn>2</mn> <mi>π</mi> </mfrac> </msqrt> <msup> <mi>e</mi> <mrow> <mo>−</mo> <mfrac> <msup> <mi>l</mi> <mn>2</mn> </msup> <mn>200</mn> </mfrac> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>∈</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>t</mi> <mo>}</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>. The parameters are given by <math display="inline"><semantics> <msub> <mi>V</mi> <mi>A</mi> </msub> </semantics></math> = 6, <math display="inline"><semantics> <mi>γ</mi> </semantics></math> = 0.2 dB/km, <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 0.01, <math display="inline"><semantics> <mi>κ</mi> </semantics></math> = 0.98, <math display="inline"><semantics> <mi>η</mi> </semantics></math> = 0.6, and <math display="inline"><semantics> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> </semantics></math> = 0.01.</p> Full article ">Figure 4
<p>The secure rates of different number of legitimate participants for <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>25</mn> </mrow> </semantics></math>. The parameters are given by <math display="inline"><semantics> <msub> <mi>V</mi> <mi>A</mi> </msub> </semantics></math> = 6, <math display="inline"><semantics> <mi>γ</mi> </semantics></math> = 0.2 dB/km, <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 0.01, <math display="inline"><semantics> <mi>κ</mi> </semantics></math> = 0.98, <math display="inline"><semantics> <mi>η</mi> </semantics></math> = 0.6, and <math display="inline"><semantics> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> </semantics></math> = 0.01.</p> Full article ">Figure 5
<p>The secret rates of different numbers of legitimate participants for <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math>. The parameters are given by <math display="inline"><semantics> <msub> <mi>V</mi> <mi>A</mi> </msub> </semantics></math> = 6, <math display="inline"><semantics> <mi>γ</mi> </semantics></math> = 0.2 dB/km, <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 0.001, <math display="inline"><semantics> <mi>κ</mi> </semantics></math> = 0.98, <math display="inline"><semantics> <mi>η</mi> </semantics></math> = 0.6, and <math display="inline"><semantics> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> </semantics></math> = 0.01.</p> Full article ">Figure 6
<p>The secret rates of different numbers of legitimate participants and reconciliation efficiency for <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math>. The parameters are given by <math display="inline"><semantics> <msub> <mi>V</mi> <mi>A</mi> </msub> </semantics></math> = 6, <math display="inline"><semantics> <mi>γ</mi> </semantics></math> = 0.2 dB/km, <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 0.005, <math display="inline"><semantics> <mi>η</mi> </semantics></math> = 0.6, and <math display="inline"><semantics> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> </semantics></math> = 0.01.</p> Full article ">Figure 7
<p>The secret rates of different numbers of legitimate participants and attenuation coefficient for <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math>. The parameters are given by <math display="inline"><semantics> <msub> <mi>V</mi> <mi>A</mi> </msub> </semantics></math> = 6, <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 0.005, <math display="inline"><semantics> <mi>κ</mi> </semantics></math> = 0.98, <math display="inline"><semantics> <mi>η</mi> </semantics></math> = 0.6, and <math display="inline"><semantics> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> </semantics></math> = 0.01.</p> Full article ">
9 pages, 262 KiB  
Article
Development of Quantum Private Queries Protocol on Collective-Dephasing Noise Channel
by Jingbo Zhao, Wenbin Zhang, Yulin Ma, Xiaohan Zhang and Hongyang Ma
Appl. Sci. 2020, 10(6), 1935; https://doi.org/10.3390/app10061935 - 12 Mar 2020
Cited by 12 | Viewed by 2348
Abstract
Quantum private queries can commonly protect important information in a good many of domains, such as finance, business, military, which use quantum effects to achieve unprecedented classical private queries. However, quantum state can be easily affected by environmental noise, which affects the actual [...] Read more.
Quantum private queries can commonly protect important information in a good many of domains, such as finance, business, military, which use quantum effects to achieve unprecedented classical private queries. However, quantum state can be easily affected by environmental noise, which affects the actual effect of quantum private queries. This paper developed a new quantum private query protocol based on four qubits logical Bell state to resist the collective-dephasing noise. The symmetric private information retrieval problem, which is the most influential problem in the process of quantum private query, was solved well by quantum oblivious transfer. It introduces the construction of four qubits logical Bell state. The quantum private query protocol innovates the quantum key distribution process by using the four qubits logical Bell state as the measurement base to measure the logical qubits, and ensures the function of quantum oblivious transmission. The protocol cannot only resist the noise influence of the communication process, but also ensure the security of both sides of the communication. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
8 pages, 1980 KiB  
Article
A Self-Stabilizing Phase Decoder for Quantum Key Distribution
by Huaxing Xu, Shaohua Wang, Yang Huang, Yaqi Song and Changlei Wang
Appl. Sci. 2020, 10(5), 1661; https://doi.org/10.3390/app10051661 - 1 Mar 2020
Cited by 1 | Viewed by 2471
Abstract
Self-stabilization quantum key distribution (QKD) systems are often based on the Faraday magneto-optic effect such as “plug and play” QKD systems and Faraday–Michelson QKD systems. In this article, we propose a new anti-quantum-channel disturbance decoder for QKD without magneto-optic devices, which can be [...] Read more.
Self-stabilization quantum key distribution (QKD) systems are often based on the Faraday magneto-optic effect such as “plug and play” QKD systems and Faraday–Michelson QKD systems. In this article, we propose a new anti-quantum-channel disturbance decoder for QKD without magneto-optic devices, which can be a benefit for the photonic integration and applications in magnetic environments. The decoder is based on a quarter-wave plate reflector–Michelson (Q–M) interferometer, with which the QKD system can be free of polarization disturbance caused by quantum channel and optical devices in the system. The theoretical analysis indicates that the Q–M interferometer is immune to polarization-induced signal fading, where the operator of the Q–M interferometer corresponding to Pauli Matrix σ2 makes it satisfy the anti-disturbance condition naturally. A Q–M interferometer based time-bin phase encoding QKD setup is demonstrated, and the experimental results show that the QKD setup works stably with a low quantum bit error rate about 1.3% for 10 h over 60.6 km standard telecommunication optical fiber. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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<p>Unbalanced-arm Michelson interferometer with two quarter-wave plate reflectors (QWPRs) as mirrors, a polarization maintaining coupler (PMC), a phase shifter (PS), and PM optical fibers.</p> Full article ">Figure 2
<p>The forward light (or incident light) and backward light (or output light) after the reflection by a QWPR, where the angle between the direction of <span class="html-italic">X</span>-polarization state, and the slow axis of the QWP (<span class="html-italic">x</span>-direction) is 45 degrees.</p> Full article ">Figure 3
<p>Double Q–M interferometers on Alice’s and Bob’s side, respectively, connected with each other by optical fiber quantum channel. LD: laser, Cir: optical circulator, PMC: polarization maintaining coupler, PS: phase shifter, QWPR: quarter-wave plate reflector, SPD: avalanche diode single photon detector, <span class="html-italic">L<sub>i</sub></span> (<span class="html-italic">i</span> = <span class="html-italic">a</span> or <span class="html-italic">b</span>): the long arm operator of the Q–M interferometer on Alice’s or Bob’s side, <span class="html-italic">S<sub>i</sub></span> (<span class="html-italic">i</span> = <span class="html-italic">a</span> or <span class="html-italic">b</span>): the short arm operator of the Q–M interferometer on Alice’s or Bob’s side.</p> Full article ">Figure 4
<p>(<b>a</b>) schematic diagram of the Q–M interferometer based time-bin phase encoding intrinsic-stabilization QKD system. The Q–M interferometers are shown in red dashed boxes. LD<sub>1</sub>–LD<sub>4</sub>: lasers, Cir<sub>1</sub> and Cir<sub>2</sub>: optical circulators, PMC<sub>1</sub> and PMC<sub>2</sub>: polarization maintaining couplers, BS<sub>1</sub>–BS<sub>4</sub>: beam splitters, PS: phase shifter, DWDM: dense wavelength division multiplexer, VOA: variable optical attenuator, SPD<sub>1</sub>–SPD<sub>4</sub>: avalanche diode single photon detectors; (<b>b</b>) the geographic distribution of the quantum channel with a 60.6 km standard telecommunication optical fiber.</p> Full article ">Figure 5
<p>Temporal fluctuation of the key generation performance. (<b>a</b>) the quantum bit error rate as a function of time; (<b>b</b>) the safe key rate as a function of time, where every point is the average safe key rate in one minute.</p> Full article ">
17 pages, 953 KiB  
Article
Quantum Dual Signature with Coherent States Based on Chained Phase-Controlled Operations
by Jinjing Shi, Shuhui Chen, Jiali Liu, Fangfang Li, Yanyan Feng and Ronghua Shi
Appl. Sci. 2020, 10(4), 1353; https://doi.org/10.3390/app10041353 - 17 Feb 2020
Cited by 3 | Viewed by 2372
Abstract
A novel encryption algorithm called the chained phase-controlled operation (CPCO) is presented in this paper, inspired by CNOT operation, which indicates a stronger correlation among message states and each message state depending on not only its corresponding key but also other message states [...] Read more.
A novel encryption algorithm called the chained phase-controlled operation (CPCO) is presented in this paper, inspired by CNOT operation, which indicates a stronger correlation among message states and each message state depending on not only its corresponding key but also other message states and their associated keys. Thus, it can prevent forgery effectively. According to the encryption algorithm CPCO and the classical dual signature protocols, a quantum dual signature scheme based on coherent states is proposed in this paper. It involves three participants, the customer Alice, the merchant Bob and the bank Trent. Alice expects to send her order message and payment message to Bob and Trent, respectively. It is required that the two messages must be linked to guarantee the payment is paid for the corresponding order. Thus, Alice can generate a quantum dual signature to achieve the goal. In detail, Alice firstly signs her two messages with the shared secret key. Then She connects the two signatures into a quantum dual signature. Finally, Bob and Trent severally verify the signatures of the order message and the payment message. Security analysis shows that our scheme can ensure its security against forgery, repudiation and denial. In addition, simulation experiments based on the Strawberry Fields platform are performed to valid the feasibility of CPCO. Experimental results demonstrate that CPCO is viable and the expected coherent states can be acquired with high fidelity, which indicates that the encryption algorithm of the scheme can be implemented on quantum devices effectively. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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<p>Schematic representation of the quantum dual signature scheme. PCOs and DPCOs separately stand for encryption and decryption based on CPCO. <math display="inline"><semantics> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </semantics></math> represents the connection operation.</p> Full article ">Figure 2
<p>The probability that all bits of the original key are 0 or 1 as a function of the length of the original key. It shows that the larger <span class="html-italic">n</span> is, the smaller probability is. Such as <span class="html-italic">n</span> is greater than 10-bit, the probability of <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mi>n</mi> </msup> </mrow> </semantics></math> approaches to 0.</p> Full article ">Figure 3
<p>The success probability of forging Alice’s signature when leaving the security probability of QKD aside. <span class="html-italic">x</span> and <span class="html-italic">y</span> represent the length of order message and payment message respectively, and <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo>≥</mo> <mn>2</mn> </mrow> </semantics></math> (bits), <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>n</mi> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>m</mi> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>m</mi> <mi>b</mi> </msub> <mo>)</mo> <mo>≥</mo> <mn>3</mn> </mrow> </semantics></math> (bits). In the light yellow box, <span class="html-italic">X</span>, <span class="html-italic">Y</span> and <span class="html-italic">Z</span> denote the values of <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>+</mo> <mi>y</mi> </mrow> </semantics></math> axis, <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>m</mi> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>m</mi> <mi>b</mi> </msub> </mrow> </semantics></math> axis and <math display="inline"><semantics> <msub> <mi>P</mi> <msub> <mi>f</mi> <mi>A</mi> </msub> </msub> </semantics></math> axis respectively.</p> Full article ">Figure 4
<p>Design schematic on the CPCOs with four input ports whose values are <math display="inline"><semantics> <mrow> <mo>|</mo> <mn>0</mn> <mo>+</mo> <mn>2</mn> <mi>i</mi> <mo>〉</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>|</mo> <mo>−</mo> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mi>i</mi> <mo>〉</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>|</mo> <mn>4</mn> <mo>+</mo> <mn>0</mn> <mi>i</mi> <mo>〉</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>|</mo> <mn>0</mn> <mo>+</mo> <mn>3</mn> <mi>i</mi> <mo>〉</mo> </mrow> </semantics></math> respectively. <math display="inline"><semantics> <msub> <mi>P</mi> <mrow> <mi>h</mi> <mi>k</mi> </mrow> </msub> </semantics></math> represents the PCO where the <span class="html-italic">h</span>-th coherent state controls the <span class="html-italic">k</span>-th coherent state. Square dots ■ in the gray virtual box represents multiple judgement conditions referred to Equation (<a href="#FD2-applsci-10-01353" class="html-disp-formula">2</a>). "HD" in the red box is the heterodyne detection [<a href="#B56-applsci-10-01353" class="html-bibr">56</a>].</p> Full article ">Figure 5
<p>Experimental results. The subfigures (<b>a</b>–<b>d</b>) represent the output of the first mode, the second mode, the third mode and the forth mode, respectively. The vertical axis indicates the probability that <span class="html-italic">x</span> or <span class="html-italic">p</span> takes a value on the horizontal axis. Besides, <span class="html-italic">x</span> and <span class="html-italic">p</span> can take the corresponding value under the maximum probability to form a coherent state.</p> Full article ">
15 pages, 521 KiB  
Article
Continuous Variable Quantum Secret Sharing with Fairness
by Ye Kang, Ying Guo, Hai Zhong, Guojun Chen and Xiaojun Jing
Appl. Sci. 2020, 10(1), 189; https://doi.org/10.3390/app10010189 - 25 Dec 2019
Cited by 3 | Viewed by 2207
Abstract
The dishonest participants have many advantages to gain others’ shares by cheating in quantum secret sharing (QSS) protocols. However, the traditional methods such as identity authentication and message authentication can not resolve this problem due to the reason that the share has already [...] Read more.
The dishonest participants have many advantages to gain others’ shares by cheating in quantum secret sharing (QSS) protocols. However, the traditional methods such as identity authentication and message authentication can not resolve this problem due to the reason that the share has already been released to dishonest participants before realizing the deception. In this paper, a continuous variable QSS (CVQSS) scheme is proposed with fairness which ensures all participants can acquire or can not acquire the secret simultaneously. The quantum channel based on two-mode squeezing states provides secure communications through which it can send shares successfully, as long as setting the squeezing and modulation parameters according to the quantum channel transmission efficiency and the Shannon information of shares. In addition, the Chinese Remainder Theorem (CRT) can provides tunable threshold structures according to demands of the complex quantum network and the strategy for fairness can be incorporated with other sharing schemes, resulting in perfect compatibility for practical implementations. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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<p>The generating of message <span class="html-italic">X</span> using secret <span class="html-italic">S</span>, checking sequence <span class="html-italic">R</span> and determine pointer <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>*</mo> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>Schematic of distribution based on two-mode squeezed vacuum state.</p> Full article ">Figure 3
<p>The information rate under different parameters (<math display="inline"><semantics> <mrow> <msup> <mo>Σ</mo> <mn>2</mn> </msup> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>).</p> Full article ">Figure 4
<p>The relation between the squeezed parameter <span class="html-italic">r</span> and the variance of message <math display="inline"><semantics> <msup> <mi>σ</mi> <mn>2</mn> </msup> </semantics></math>, when <math display="inline"><semantics> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <mi>S</mi> <mo>,</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mo form="prefix">log</mo> <mn>2</mn> </msub> <mn>3</mn> </mrow> </semantics></math> bit.</p> Full article ">Figure 5
<p>The mutual information of Eve.</p> Full article ">Figure 6
<p>The information rate under attack (<math display="inline"><semantics> <mrow> <msup> <mo>Σ</mo> <mn>2</mn> </msup> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>).</p> Full article ">Figure 7
<p>The relation between the squeezed parameter <span class="html-italic">r</span> and the variance of message <math display="inline"><semantics> <msup> <mi>σ</mi> <mn>2</mn> </msup> </semantics></math>, when <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <mi>I</mi> <mo>=</mo> <msub> <mo form="prefix">log</mo> <mn>2</mn> </msub> <mn>3</mn> </mrow> </semantics></math> bit.</p> Full article ">
11 pages, 1005 KiB  
Article
Performance Analysis of the Shore-to-Reef Atmospheric Continuous-Variable Quantum Key Distribution
by Shujing Zhang, Chen Xiao, Chun Zhou, Xiang Wang, Jianshu Yao, Hailong Zhang and Wansu Bao
Appl. Sci. 2019, 9(24), 5285; https://doi.org/10.3390/app9245285 - 4 Dec 2019
Cited by 1 | Viewed by 1774
Abstract
The effects of sea salt concluded in oceanic atmosphere are ubiquitous in practical wireless optical links. Here a shore-to-reef atmospheric continuous-variable quantum key distribution (CVQKD) model is established on the basis of Mie scattering theory, with the aim to characterize the complex case [...] Read more.
The effects of sea salt concluded in oceanic atmosphere are ubiquitous in practical wireless optical links. Here a shore-to-reef atmospheric continuous-variable quantum key distribution (CVQKD) model is established on the basis of Mie scattering theory, with the aim to characterize the complex case of beam propagation in the atmosphere caused by sea salt particles. The effects on performance of shore-to-reef atmospheric CVQKD under the sea salt particles and relative humidity are also studied. Simulation results show that the increase of particle radius and relative humidity will lead to the degeneration of secret key rate. Extending the channel distance also reduces the secret key rate. This paper provides a basis for the establishment of practical shore-to-reef atmospheric CVQKD model. The research of this paper also gives momentous reference for the study of optical communication channel models with other suspended particles over the ocean. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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<p>Continuous-variable quantum key distribution (CVQKD) through shore-to-reef atmospheric channel.</p> Full article ">Figure 2
<p>Beam wandering and broadening.</p> Full article ">Figure 3
<p>The refraction structure at altitudes of <span class="html-italic">h</span> = 0 km, <span class="html-italic">h</span> = 1 km, <span class="html-italic">h</span> = 10 km, and <span class="html-italic">h</span> = 20 km with various wind speeds.</p> Full article ">Figure 4
<p>The relationship between particle radius and extinction coefficient. The transmission distance of sea surface is 10 km and the relative humidity is <math display="inline"><semantics> <mrow> <mn>80</mn> <mo>%</mo> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>(<b>a</b>) The relationship between secret key rate and relative humidity, where the distance of shore-based is invariable and the sea salt radius is 0.5 m. (<b>b</b>) Secret key rate versus relative humidity, where the distance of sea surface is invariable and sea salt radius is 0.5 m. (<b>c</b>) Secret key rate versus sea salt radius, where the distance of shore-based is invariable and relative humidity is <math display="inline"><semantics> <mrow> <mn>80</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>d</b>) The relationship between secret key rate and sea salt radius, where relative humidity is <math display="inline"><semantics> <mrow> <mn>80</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>e</b>) Behavior of the secret key rate in terms of relative humidity and sea salt radius, when the distance of sea surface is 1 km, 2 km, 3 km, 5 km, 8 km, and 10 km, while the distance of shore-based is invariable. (<b>f</b>) Secret key rate as a function of relative humidity and sea salt radius, where the distance of shore-based is 1 km, 2 km, 3 km, 5 km, 8 km, and 10 km, respectively.</p> Full article ">
19 pages, 3540 KiB  
Article
Security Analysis of Discrete-Modulated Continuous-Variable Quantum Key Distribution over Seawater Channel
by Xinchao Ruan, Hang Zhang, Wei Zhao, Xiaoxue Wang, Xuan Li and Ying Guo
Appl. Sci. 2019, 9(22), 4956; https://doi.org/10.3390/app9224956 - 18 Nov 2019
Cited by 16 | Viewed by 3385
Abstract
We investigate the optical absorption and scattering properties of four different kinds of seawater as the quantum channel. The models of discrete-modulated continuous-variable quantum key distribution (CV-QKD) in free-space seawater channel are briefly described, and the performance of the four-state protocol and the [...] Read more.
We investigate the optical absorption and scattering properties of four different kinds of seawater as the quantum channel. The models of discrete-modulated continuous-variable quantum key distribution (CV-QKD) in free-space seawater channel are briefly described, and the performance of the four-state protocol and the eight-state protocol in asymptotic and finite-size cases is analyzed in detail. Simulation results illustrate that the more complex is the seawater composition, the worse is the performance of the protocol. For different types of seawater channels, we can improve the performance of the protocol by selecting different optimal modulation variances and controlling the extra noise on the channel. Besides, we can find that the performance of the eight-state protocol is better than that of the four-state protocol, and there is little difference between homodyne detection and heterodyne detection. Although the secret key rate of the protocol that we propose is still relatively low and the maximum transmission distance is only a few hundred meters, the research on CV-QKD over the seawater channel is of great significance, which provides a new idea for the construction of global secure communication network. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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<p>(Color online.) The attenuation coefficients of the four different types of seawater as functions of wavelength of the signal light. The blue dashed line, the green dashed line, and the red solid line represent the change curves of the absorption coefficient <math display="inline"> <semantics> <mrow> <mi>a</mi> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </semantics> </math>, the scattering coefficient <math display="inline"> <semantics> <mrow> <mi>b</mi> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </semantics> </math>, and the total attenuation coefficient <math display="inline"> <semantics> <mrow> <mi>c</mi> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </semantics> </math>, respectively.</p> Full article ">Figure 2
<p>(Color online.) Light intensity distribution at different transmission distances of the four-state protocol over a pure sea water channel: (<b>a</b>–<b>c</b>) the three-dimensional views of the intensity distribution of the signal light at the position of initial, 8 m, and 20 m of the seawater channel, respectively; and (<b>d</b>–<b>f</b>) are their corresponding plane views.</p> Full article ">Figure 2 Cont.
<p>(Color online.) Light intensity distribution at different transmission distances of the four-state protocol over a pure sea water channel: (<b>a</b>–<b>c</b>) the three-dimensional views of the intensity distribution of the signal light at the position of initial, 8 m, and 20 m of the seawater channel, respectively; and (<b>d</b>–<b>f</b>) are their corresponding plane views.</p> Full article ">Figure 3
<p>Three link models of end-to-end underwater CV-QKD system.</p> Full article ">Figure 4
<p>The entanglement-based scheme of the discrete-modulated underwater CV-QKD. Alice randomly prepares one of the <span class="html-italic">N</span> states and sends it to Bob through the untrusted seawater channel. Bob detects the received model to derive a sequence of bits shared with Alice by using a homodyne detector or a heterodyne detector. The seawater channel is assumed to be a linear channel.</p> Full article ">Figure 5
<p>(Color online.) Secret key rate of the four-state protocol for realistic reconciliation efficiency of <math display="inline"> <semantics> <mrow> <mn>90</mn> <mo>%</mo> </mrow> </semantics> </math> and a quantum efficiency of Bob’s detection equal to <math display="inline"> <semantics> <mrow> <mn>0.6</mn> </mrow> </semantics> </math> with thermal noise <math display="inline"> <semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mspace width="3.33333pt"/> <mo>=</mo> <mspace width="3.33333pt"/> <mn>0.01</mn> </mrow> </semantics> </math>. <math display="inline"> <semantics> <mrow> <msub> <mi>V</mi> <mi>A</mi> </msub> <mspace width="3.33333pt"/> <mo>=</mo> <mspace width="3.33333pt"/> <mn>0.6</mn> <mo>,</mo> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics> </math> (in shot-noise unit).</p> Full article ">Figure 6
<p>(Color online.) Secret key rate of the eight-state protocol for realistic reconciliation efficiency of <math display="inline"> <semantics> <mrow> <mn>90</mn> <mo>%</mo> </mrow> </semantics> </math> and a quantum efficiency of Bob’s detection equal to <math display="inline"> <semantics> <mrow> <mn>0.6</mn> </mrow> </semantics> </math> with thermal noise <math display="inline"> <semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics> </math>. <math display="inline"> <semantics> <mrow> <msub> <mi>V</mi> <mi>A</mi> </msub> <mo>=</mo> <mspace width="3.33333pt"/> <mn>0.6</mn> <mo>,</mo> <mi>ε</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics> </math> (in shot-noise unit).</p> Full article ">Figure 7
<p>(Color online.) The maximum tolerable excess noise at each distance for four-state protocol. <math display="inline"> <semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <msub> <mi>V</mi> <mi>A</mi> </msub> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <mi>η</mi> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 8
<p>(Color online.) The maximum tolerable excess noise at each distance for eight-state protocol. <math display="inline"> <semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <msub> <mi>V</mi> <mi>A</mi> </msub> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <mi>η</mi> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 9
<p>(Color online.) The compressed variation trend of <math display="inline"> <semantics> <msub> <mi>V</mi> <mi>A</mi> </msub> </semantics> </math> optimal interval of the four-state protocol as the transmission distance extends. <math display="inline"> <semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <mi>ε</mi> <mo>=</mo> <mn>0.005</mn> <mo>,</mo> <mi>η</mi> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 10
<p>(Color online.) The compressed variation trend of <math display="inline"> <semantics> <msub> <mi>V</mi> <mi>A</mi> </msub> </semantics> </math> optimal interval of the eight-state protocol as the transmission distance extends. <math display="inline"> <semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <mi>ε</mi> <mo>=</mo> <mn>0.005</mn> <mo>,</mo> <mi>η</mi> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <msub> <mi>v</mi> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 11
<p>(Color online.) The finite-size and the asymptotic secret key rate of the four-state underwater CV-QKD protocol. From left to right in every sub-figure, curves of different colors correspond, respectively, to block lengths of <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>8</mn> </msup> </semantics> </math>, <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>10</mn> </msup> </semantics> </math>, <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>12</mn> </msup> </semantics> </math>, and <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>14</mn> </msup> </semantics> </math>, and the asymptotic curves.</p> Full article ">Figure 11 Cont.
<p>(Color online.) The finite-size and the asymptotic secret key rate of the four-state underwater CV-QKD protocol. From left to right in every sub-figure, curves of different colors correspond, respectively, to block lengths of <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>8</mn> </msup> </semantics> </math>, <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>10</mn> </msup> </semantics> </math>, <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>12</mn> </msup> </semantics> </math>, and <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>14</mn> </msup> </semantics> </math>, and the asymptotic curves.</p> Full article ">Figure 12
<p>(Color online.) The finite-size and the asymptotic secret key rate of the eight-state underwater CV-QKD protocol. From left to right in every sub-figure, curves of different colors correspond, respectively, to block lengths of <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>8</mn> </msup> </semantics> </math>, <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>10</mn> </msup> </semantics> </math>, <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>12</mn> </msup> </semantics> </math>, and <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>14</mn> </msup> </semantics> </math>, and the asymptotic curves.</p> Full article ">
15 pages, 753 KiB  
Article
Continuous-Variable Quantum Key Distribution Robust Against Polarization-Dependent Loss
by Ying Guo, Minglu Cai and Duan Huang
Appl. Sci. 2019, 9(18), 3937; https://doi.org/10.3390/app9183937 - 19 Sep 2019
Viewed by 3892
Abstract
Polarization is one of the physical characteristics of optical waves, and the polarization-division-multiplexing (PDM) scheme has gained much attraction thanks to its capability of achieving high transmission rate. In the PDM-based quantum key distribution (QKD), the key information could be encoded independently by [...] Read more.
Polarization is one of the physical characteristics of optical waves, and the polarization-division-multiplexing (PDM) scheme has gained much attraction thanks to its capability of achieving high transmission rate. In the PDM-based quantum key distribution (QKD), the key information could be encoded independently by the optical fields E x and E y , where the 2-dimensional modulation and orthogonal polarization multiplexing usually result in two-fold channel capacity. Unfortunately, the non-negligible polarization-dependent loss (PDL) caused by the crystal dichroism in optical devices may result in the signal distortion, leading to an imbalanced optical signal-to-noise ratio. Here, we present a polarization-pairwise coding (PPC) scheme for the PDM-based continuous-variable (CV) QKD systems to overcome the PDL problem. Numerical simulation results indicate that the PDL-induced performance degradation can be mitigated. In addition, the PPC scheme, tailored to be robust against a high level of PDL, offers a suitable solution to improve the performance of the PDM-based CVQKD in terms of the secret key rate and maximal transmission distance. Full article
(This article belongs to the Special Issue Quantum Communications and Quantum Networks)
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Figure 1
<p>(Color online.) (<b>a</b>) The discretely modulated PDM-based continuous-variable quantum key distribution (CVQKD) system. PBS: polarization beam splitter. PBC: polarization beam combiner. LO: local oscillation. (<b>b</b>) The transmission of two polarizations. The orthogonality of two polarizations is destroyed due to the non-negligible polarization dependent loss (PDL).</p> Full article ">Figure 2
<p>(Color online.) (<b>a</b>) Schematic PDL diagram. After transmission, two polarization states lose their orthogonality, with the different loss in their polarization directions. (<b>b</b>) PDL distributed model. PDLE: PDL emulator. ASE: amplified spontaneous emission.</p> Full article ">Figure 3
<p>(<b>a</b>) The effect of PDL on the components of the electric. (<b>b</b>) Orthogonality of two polarizations with increase of <math display="inline"><semantics> <mi>μ</mi> </semantics></math>.</p> Full article ">Figure 4
<p>(Color online.) Polarization-division-multiplexing (PDM)-quadrature phase shift modulation (QPSK) optical transmitter.</p> Full article ">Figure 5
<p>(Color online.) The polarization-pairwise coding (PPC)-based CVQKD system with PDM-QPSK. (<b>a</b>) Transmitter polarization-pairwise pre-coding. (<b>b</b>) Receiver polarization-pairwise decoding.</p> Full article ">Figure 6
<p>Signal-to-noise ratio (SNR) difference between two polarizations due to PDL.</p> Full article ">Figure 7
<p>The resulting error rate with SNR for <math display="inline"><semantics> <mrow> <mo>△</mo> <mi>S</mi> <mi>N</mi> <mi>R</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math><math display="inline"><semantics> <mrow> <mi>d</mi> <mi>B</mi> </mrow> </semantics></math>.</p> Full article ">Figure 8
<p>The <math display="inline"><semantics> <mrow> <mi>I</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>:</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> with SNR for <math display="inline"><semantics> <mrow> <mo>△</mo> <mi>S</mi> <mi>N</mi> <mi>R</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math><math display="inline"><semantics> <mrow> <mi>d</mi> <mi>B</mi> </mrow> </semantics></math>.</p> Full article ">Figure 9
<p>Parameter relationships in the PDM-based system. (<b>a</b>) The secret key rate as a function of modulation variance <math display="inline"><semantics> <msub> <mi>V</mi> <mi>M</mi> </msub> </semantics></math> in different excess noise with transmission distance d = 100 km. (<b>b</b>) The secret key rate as a function of excess noise in different modulation variance <math display="inline"><semantics> <msub> <mi>V</mi> <mi>M</mi> </msub> </semantics></math> with transmission distance d = 100 km.</p> Full article ">Figure 10
<p>The secret key rate as a function of transmission distance.</p> Full article ">Figure A1
<p>The resulting BER of single-channel for △SNR<math display="inline"><semantics> <mrow> <mo>∈</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>6</mn> <mo>,</mo> <mn>9</mn> <mo>}</mo> </mrow> </semantics></math> dB.</p> Full article ">
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