Quantum key distribution provides secure keys with information-theoretic security ensured by the principle of quantum mechanics. The continuous-variable version of quantum key distribution using coherent states offers the advantages of its compatibility with telecom industry, e.g., using commercial laser and homodyne detector, is now going through a booming period. In this review article, we describe the principle of continuous-variable quantum key distribution system; focus on protocols based on coherent states, whose systems are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. We start by reviewing the theoretical protocols and the current security status of these protocols. Then, we discuss the system structure, the key module, and the mainstream system implementations. The advanced progresses for future applications are discussed, including the digital techniques, system on chip, and point-to-multipoint system. Finally, we discuss the practical security of the system and conclude with promising perspectives in this research field. 

https://pubs.aip.org/aip/apr/article-pdf/doi/10.1063/5.0179566/19855574/011318_1_5.0179566.pdf

Continuous-variable quantum key distribution system: Past, present, and future

Quantum key distribution (QKD) enables two authenticated parties to share secret keys with the ability to detect any attempts to eavesdrop the keys theoretically. As a crucial step, information reconciliation protocol has a significant effect on the secret key rate and maximal transmission distance of continuous-variable quantum key distribution (CV-QKD) systems. To improve the secret key rate in practical CV-QKD systems with time-varying quantum channel, we propose an efficient rate-adaptive multidimensional information reconciliation protocol based on polar codes. Simulation results verify that our proposed rate-adaptive reconciliation protocol can enhance the secret key rate compared to that of the conventional reconciliation protocol.

Rate-adaptive reconciliation with polar coding for continuous-variable quantum key distribution

The well-known multidimensional reconciliation is a significant stage of a continuous-variable quantum key distribution (CVQKD) system, which uses $d$-dimensional rotations to build a virtual channel between authenticated parties, Alice and Bob. Generally, a block low-density parity-check code with a belief-propagation (BP) iterative decoding algorithm, which is optimized for an additive white Gaussian noise channel, is always used in multidimensional reconciliation for the CVQKD system. In this paper, we study the signal-to-noise ratio (SNR) of the virtual channel of multidimensional reconciliation in CVQKD and prove that the noise of the virtual channel follows the Student's $t$-distribution. Therefore, we propose a $t$-BP decoding algorithm, which can be better applied to multidimensional reconciliation. Simulation results show that the frame error rate (FER) with the proposed $t$-BP decoding algorithm is superior to that with the conventional BP decoding algorithm applied to multidimensional reconciliation. Subsequently, the FER improvement results in significant influence on reconciliation efficiency and secret key rate of the CVQKD system.

Virtual channel of multidimensional reconciliation in a continuous-variable quantum key distribution

Abstract Quantum key distribution (QKD) can provide information-theoretically secure keys for two parties of legitimate communication, and information reconciliation, as an indispensable component of QKD systems, can correct errors present in raw keys based on error-correcting codes. In this paper, we first describe the basic knowledge of information reconciliation and its impact on continuous variable QKD. Then we introduce the information schemes and the corresponding error correction codes employed. Next, we introduce the rate-compatible codes, the hardware acceleration of the reconciliation algorithm, the research progress of information reconciliation, and its application in continuous variable QKD. Finally, we discuss the future challenges and conclude. 

Information reconciliation of continuous-variables quantum key distribution: principles, implementations and applications


 In continuous-variable quantum key distribution systems, reconciliation is a crucial step that significantly affects the secret key rate (SKR). The rateless protocol based on Raptor codes can achieve high reconciliation efficiency at low signal-to-noise ratios (SNRs). However, the high complexity of low-density parity-check (LDPC) codes used for the precoding in Raptor codes limits the speed of reconciliation. In this paper, we propose an adaptive reconciliation protocol by modifying Raptor codes. The length of random binary sequences is increased because we remove the LDPC precoding that adds redundancy. The modified Raptor codes reduce the complexity of encoding with better performance. The proposed protocol can achieve a reconciliation efficiency of 98.1% and reach a SKR higher than 2.5×10^3 bit/s at a SNR of -20dB, higher than previous protocols.

Low-Complexity Adaptive Reconciliation Protocol for Continuous-Variable Quantum Key Distribution

Due to the rapid development of quantum computing technology, encryption systems based on computational complexity are facing serious threats. Based on the fundamental theorem of quantum mechanics, continuous-variable quantum key distribution (CVQKD) has the property of physical absolute security and can effectively overcome the dependence of the current encryption system on the computational complexity. In this paper, we construct the spatially coupled (SC)-low-density parity-check (LDPC) codes and quasi-cyclic (QC)-LDPC codes by adopting the parity-check matrices of LDPC codes in the Advanced Television Systems Committee (ATSC) 3.0 standard as base matrices and introduce these codes for information reconciliation in the CVQKD system in order to improve the performance of reconciliation efficiency, and then make further improvements to final secret key rate and transmission distance. Simulation results show that the proposed LDPC codes can achieve reconciliation efficiency of higher than 0.96. Moreover, we can obtain a high final secret key rate and a long transmission distance through using our proposed LDPC codes for information reconciliation.

High Efficiency Continuous-Variable Quantum Key Distribution Based on ATSC 3.0 LDPC Codes

Information reconciliation in the continuousvariable quantum key distribution (CVQKD) plays a vital role on affecting secret key rate as well as maximum transmission distance. It is necessary to search good error-correcting codes in order to improve the performance of reconciliation efficiency. In this work, we construct Quasi-Cyclic (QC) low-density paritycheck (LDPC) codes based on LDPC codes in the digital video broadcasting second generation terrestrial (DVB-T2) standard, and then combine these codes with information reconciliation in the CVQKD system, which can extremely ameliorate the performance of secret key rate and maximum transmission distance. The simulation results show that our proposed QC-LDPC codes can achieve higher reconciliation efficiency of 93.05% compare to DVB-T2 LDPC codes, which means our proposed QC-LDPC codes can obtain better performance of secret key rate and longer maximum transmission distance.

High Efficiency Continuous-Variable Quantum Key Distribution Based on Quasi-Cyclic LDPC Codes

Secret key rate of continuous-variable quantum key distribution with finite codeword length

In continuous-variable quantum key distribution (CV-QKD) systems, information reconciliation (IR) is a crucial step that significantly affects the secret key rate (SKR). The fixed-rate error-correcting codes used in IR are highly sensitive to changes in the signal-to-noise ratio (SNR) and cannot maintain a high reconciliation efficiency in practical CV-QKD systems. To address this issue, we first propose a rate-adaptive IR protocol, namely Threshold-based IR (TIR), which changes the code rate of low-density parity-check (LDPC) codes by selectively revealing bits with lower reliability and adjusting their log-likelihood ratios (LLRs). Then, we propose a rate-adaptive IR protocol, namely Sorting-based IR (SIR), which not only adjusts the code rate according to variations in SNR, but also enables the CV-QKD systems to achieve high reconciliation efficiency over a wide range of SNRs. Furthermore, we perform an analysis of the protocols in terms of code rate, reconciliation efficiency, and complexity. The simulation results demonstrate that the proposed protocols outperform other rate-adaptive IR protocols, achieving a reconciliation efficiency higher than 98.5% in the SNR range below −20 dB and maintaining a certain SKR in long-distance transmission.

Rate-Adaptive Information Reconciliation for CV-QKD Systems at Low Signal-to-Noise Ratios

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