基于双边类型低密度奇偶校验码的连续变量量子密钥分发多维数据协调
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摘要
在连续变量量子密钥分发(CVQKD)多维数据协调过程中,低密度奇偶校验码(LDPC)的纠错性能直接影响协调效率和传输距离。构造了一种双边类型的低密度奇偶校验码(TET-LDPC),引入了类似于重复累积码中的累积结构以提高其纠错性能,在多维数据协调算法中得到了更小的收敛信噪比、更高的协调效率以及更远的传输距离。仿真结果表明:当TET-LDPC的码率为0.5,分组码长为2×10~5时,收敛信噪比降至1.02dB,协调效率达到了98.58%,安全密钥率达到17.61kb/s,CVQKD系统的传输距离提高为44.9km。
In the multidimensional reconciliation process of continuous-variable quantum key distribution(CVQKD),the error correction performance of the low-density parity-check code(LDPC)directly affects the reconciliation efficiency and transmission distance.Herein,a two-edge type low-density parity-check code(TET-LDPC)is constructed.We introduce a cumulative structure similar to that of a repeat-accumulate code into the TET-LDPC to improve its error correction performance.These codes obtain a smaller convergence signal-to-noise ratio,whereas the reconciliation system achieves higher coordination efficiency and longer transmission distance.The simulation results indicate that at a TET-LDPC code rate of 0.5 and a block length of 2×10~5,the convergence signal-to-noise ratio of the system is reduced to 1.02 dB,the data reconciliation efficiency is 98.58%,the security key rate reaches17.61 kb/s,and the CVQKD transmission distance increases to 44.9 km.
In the multidimensional reconciliation process of continuous-variable quantum key distribution(CVQKD),the error correction performance of the low-density parity-check code(LDPC)directly affects the reconciliation efficiency and transmission distance.Herein,a two-edge type low-density parity-check code(TET-LDPC)is constructed.We introduce a cumulative structure similar to that of a repeat-accumulate code into the TET-LDPC to improve its error correction performance.These codes obtain a smaller convergence signal-to-noise ratio,whereas the reconciliation system achieves higher coordination efficiency and longer transmission distance.The simulation results indicate that at a TET-LDPC code rate of 0.5 and a block length of 2×10~5,the convergence signal-to-noise ratio of the system is reduced to 1.02 dB,the data reconciliation efficiency is 98.58%,the security key rate reaches17.61 kb/s,and the CVQKD transmission distance increases to 44.9 km.
引文
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[2]Guo H,Li Z Y,Peng X.Quantum cryptography[M].Beijing:National Defense Industry Press,2006:234-309.郭弘,李政宇,彭翔.量子密码[M].北京:国防工业出版社,2016:234-309.
[3]Ralph T C.Continuous variable quantum cryptography[J].Physics Review A,2000,61(1):010303.
[4]Hillery M.Quantum cryptography with squeezed states[J].Physical Review A,2000,61(2):022309.
[5]Grosshans F,Van Assche G,Wenger J,et al.Quantum key distribution using Gaussian-modulated coherent states[J].Nature,2003,421(6920):238-241.
[6]Gong L H,Song H C,He C S,et al.A continuous variable quantum deterministic key distribution based on two-mode squeezed states[J].Physica Scripta,2014,89(3):035101.
[7]Wang J J,Jia X J,Peng K C.Improvement of balanced homodyne detector[J].Acta Optica Sinica,2012,32(1):0127001.王金晶,贾晓军,彭堃墀.平衡零拍探测器的改进[J].光学学报,2012,32(1):0127001.
[8]Ma L X,Qin J L,Yan Z H,et al.Fast response balanced homodyne detector for continuous-variable quantum memory[J].Acta Optica Sinica,2018,38(2):0227001马丽霞,秦际良,闫智辉,等.用于连续变量量子存储的快速响应平衡零拍探测器[J].光学学报,2018,38(2):0227001.
[9]Lodewyck J,Bloch M,Garcia-Patron R,et al.Quantum key distribution over 25km with an allfiber continuous-variable system[J].Physical Review A,2007,76(4):042325.
[10]Wang C,Huang D,Huang P,et al.25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel[J].Scientific Reports,2015,5:14607.
[11]Wang X Y,Bai Z L,Wang S F,et al.Four-states modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise[J].China Physical Letter,2013,30(1):010305.
[12]Li Y M,Wang X Y,Bai Z L,et al.Continuous variable quantum key distribution[J].Chinese Physics B,2017,26(4):040303.
[13]Zhao S M,Shen Z G,Xiao H,et al.Multidimensional reconciliation protocol for continuous-variable quantum key agreement with polar coding[J].Science China Physics,Mechanics&Astronomy,2018,61(9):90323.
[14]Van Assche G,Cardinal J,Cerf N J,et al.Reconciliation of a quantum-distributed Gaussian key[J].IEEE Transactions on Information Theory,2004,50(2):394-400.
[15]Leverrier A,Alléaume R,Boutros J,et al.Multidimensional reconciliation for a continuous variable quantum key distribution[J].Physical Review A,2008,77(4):042325.
[16]Wang Y Y,Guo D B,Zhang Y H,et al.Algorithm of multidimensional reconciliation for continuousvariable quantum key distribution[J].Acta Optica Sinica,2014,34(8):0827002.王云艳,郭大波,张彦煌,等.连续变量量子密钥分发多维数据协调算法[J].光学学报,2014,34(8):0827002.
[17]Dou L,Guo D B,Wang X K.Optimizing multidimensional reconciliation algorithm for continuous-variable quantum key distribution[J].Acta Optica Sinica,2016,36(9):0927001.窦磊,郭大波,王晓凯.连续变量量子密钥分发多维数据协调算法优化[J].光学学报,2016,36(9):0927001.
[18]Leverrier A,Grangier P.Continuous-variable quantum-key-distribution protocols with a nonGaussian modulation[J].Physical Review A,2011,83(4):042312.
[19]Jouguet P,Kunz-Jacques S,Leverrier A,et al.Long-distance continuous variable quantum key distribution with a Gaussian modulation[J].Physical Review A,2011,84(6):062317.
[20]Gallager R.Low-density parity-check codes[J].IEEETransactions on Information Theory,1962,8(1):21-28.
[21]David J,Mackay C,Radford M,et al.Good codes based on very sparse matrices[C]∥IMA International Conference on Cryptography and Coding,December1,1995,Cirencester,United Kingdom.Berlin,Heidelberg:Springer,1995,1025:100-111.
[22]Hu X Y,Eleftheriou E,Arnold D M.Progressive edge-growth Tanner graphs[C]∥GLOBECOM'01.IEEE Global Telecommunications Conference(Cat.no.01CH37270),November 25-29,2001,San Antonio,TX,USA.New York:IEEE,2001:995-1001.
[23]Hu X Y,Elefthefiou E,Arnold D M.Regular and irregular progressive edge-growth tanner graphs[J].IEEE Transactions on Information Theory,2005,51(1):386-398.
[24]Richardson T.Modern coding theory[M].Cambridge:Cambridge University Press,2008:381-480.
[25]Richardson T J,Urbanke R L,et al.The capacity of low-density parity-check codes under message-passing decoding[J].IEEE Transactions on Information Theory,2001,47(2):599-618.
[26]Shokrollahi A,Storn R.Design of efficient erasure codes with differential evolution[C]∥2000 IEEEInternational Symposium on Information Theory(Cat.no.00CH37060),June 25-30,2000,Sorrento,Italy.New York:IEEE,2000:866295.