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

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

In continuous-variable (CV) quantum key distribution (QKD), the reconciliation efficiency and frame error rate of the information reconciliation have a significant impact on the secret key rate. For a fixed-rate multiedge-type low-density parity-check (LDPC) code, the reconciliation efficiency and frame error rate will inevitably vary due to the fluctuations of the signal-to-noise ratio (SNR) of the CV QKD system, which degrades the performance of the system. We propose a high-efficiency rate-adaptive information reconciliation scheme by combining raptorlike (RL) LDPC codes with the addition of trusted noises. We establish the model of adding trusted noises and combine it with the RL LDPC codes to optimize the secret key rate under the time-varying channel. The simulation results show that our scheme can maintain a high reconciliation efficiency of more than 94.4% and a low frame error rate within 15% fluctuation range of the SNR. Furthermore, we implement the hardware acceleration of the proposed rate-adaptive scheme on a graphics processing unit and achieve a decoding throughput of 65.5 Mbits/s by optimizing the storage of the parity-check matrix. Our results are useful for the practical CV QKD under the realistic time-varying channel. 

High-efficiency rate-adaptive reconciliation in continuous-variable quantum key distribution

The use of quaternion orthogonal designs (QODs) to describe point-to-point communication among dual-polarized antennas has the potential to provide higher rate orthogonal and quasi-orthogonal complex designs exploiting polarization diversity among space and time diversities. Furthermore, it is essential to have a space time block code (STBC) which offers a linear and decoupled decoder which quasi-orthogonal designs fail to attain. In this paper, we show how the realm of quaternions unexpectedly offers us a possible solution and codes obtained from quaternion designs mostly achieve both linear and decoupled decoders. This motivated us to perform an indispensable search for QODs such that the code rate is bounded below by 1/2 and does not sharply decrease as the number of transmit antennas increases. It is shown that three famous recursive techniques do not satisfy this criteria and their code rates decrease rather rapidly. Therefore, we propose another method of constructing quaternion designs suitable for any number of transmit antennas and verify that these attain linear and decoupled decoders with the system model based on quaternionic channel. It is shown that such designs outperform others in terms of transmit diversity, code rates and the optimality of the proposed decoder is validated through simulation results.

/pdf/quaternion-codes-in-mimo-system-of-dual-polarized-antennas-1h9w4dbq9x.pdf

Quaternion Codes in MIMO System of Dual-Polarized Antennas

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

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

In this letter, we propose a dual-polarized precoding-aided spatial modulation (DPPSM) scheme, which introduces the polarization dimension into conventional precoding-aided spatial modulation (PSM) to transmit an additional information bit, avoiding the occupation of additional physical space while offering extra transmit diversity. We obtain an upper bound on the average bit error probability (ABEP) of the proposed DPPSM scheme over correlated fading channels. We also derive an approximate upper bound on the ABEP to show the diversity order. Simulation results show that the upper bound is tight for a high signal-to-noise ratio (SNR) range, and the bit error rate (BER) performance of the proposed DPPSM scheme is better than that of the conventional PSM scheme at the same spectral efficiency when equipped with an equal amount of antennas. Furthermore, the proposed DPPSM scheme is more robust to Gaussian channel error when the channel estimation imperfection is considered.

Precoding-Aided Spatial Modulation With Dual-Polarized Antennas Over Correlated Channels

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Papers

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

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

Precoding-Aided Spatial Modulation With Dual-Polarized Antennas Over Correlated Channels