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高效误码纠错是量子密钥分配后续数据处理的关键技术之一.基于汉明码校验子级联单向一次通信纠错方案, 分别对三种校验子级联纠错能力进行了理论和仿真分析.根据分析结果提出了一种基于混合校验子级联纠错协议, 通过优化纠错流程相关参数提高密钥生成效率.随后对该协议的纠错能力及其密钥生成效率进行了仿真分析, 最后根据误码率后验分布参数, 对密钥最终误码率及其置信区间进行了估计.单一校验子级联纠错仿真结果显示:在相同的纠错能力的条件下, 初始误码率为3% p ≤ 11% 时, (7, 4)汉明码纠错的密钥生成效率最高;初始误码率为1.5% p ≤ 3.0% 时, (15, 11)汉明码纠错的密钥生成效率最高;初始误码率为p ≤ 1.5% 时, (31, 26) 汉明码纠错的密钥生成效率最高.混合校验子级联纠错方案的仿真结果显示:对于初始误码率为9.50%, 经过8轮次混合校验子级联纠错, 密钥生成效率为9.94%, 误码率期望值为5.21×10-12, 置信度为90%的上限值为2.85×10-11, 相比用单一(7, 4)校验子级联纠错的密钥生成效率提高了约3倍.Higher efficiency of error reconciliation technique is for data post-processing for quantum key distribution. Based on the one way error reconciliation scheme of Hamming syndrome concatenation, the error correction performances of there kinds of Hamming codes are demonstrated by data simulation analysis. The simulation results indicate that when the initial error rates are (-∞, 1.5%], (1.5%, 3%], and (3%, 11%], if using Hamming (31, 26), (15, 11), and (7, 4) codes to correct the errors, respectively, the key generation rate is maximized. Base on these outcomes, we propose a kind of modified error reconciliation scheme which is based on the mixed pattern of Hamming syndrome concatenation. The ability to correct the errors and the key generation rate are verified through data simulation. Meanwhile, using the parameters of the posterior distribution based on the tested data, a simple method of estimating bit error rates (BER) with a confidence interval is estimated. The simulation results show that when the initial bit error rate is 9.50%, after correcting error 8 times error, the error bits are eliminated completely and the key generation rate is 9.94%. The BER expectation is 5.21×10-12, when the confidence is 90% the corresponding upper limit of BER is 2.85×10-11. The key generation rate increased by about 3-fold compared with that of original error reconciliation scheme.
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Keywords:
- quantum key distribution /
- error reconciliation /
- efficiency analysis
[1] Gisin N, Ribordy G, Wolfgang T, Zbinden H 2002 Rev. Mod. Phys. 74 145
[2] Zhao F, Li J L 2010 J. Optoelectronics·Laser 21 1383 (in Chinese) [赵峰, 李静玲 2010 光电子·激光 21 1383]
[3] Li S, Ma H Q, Wu L A, Zhai G J 2013 Acta Phys. Sin. 62 084214 (in Chinese) [李申, 马海强, 吴令安, 翟光杰 2013 62 084214]
[4] Yue X L, Wang J D, Wei Z J, Guo B H, Liu S H 2012 Acta Phys. Sin. 61 184215 (in Chinese) [岳孝林, 王金东, 魏正军, 郭邦红, 刘颂豪 2012 61 184215]
[5] Jiao R Z, Tang S J, Zhang C 2012 Acta Phys. Sin. 61 050302 (in Chinese) [焦荣珍, 唐少杰, 张弨 2012 61 050302]
[6] Bennett C, Bessette F, Brassard G, Salvail L, Smolin J 1992 J. Cryptol. 5 3
[7] Brassard G, Salvail L 1994 Advances in Cryptology–EUROCRYPT ’93 Norway, May 23-27, 1993 p410
[8] Buttler W T, Lamoreaux S K, Torgerson J R, Nickel G H, Donahue C H, Peterson C G 2003 Phys. Rev. A 67 052303
[9] Biham E, Boyer M, Boykin P, Mor T, Roychowdhury V 2006 J. Cryptol. 19 381
[10] Mayers D 2011 J. ACM 48 351
[11] Liu D, Yin Z Q, Wang S, Wang F M, Chen W, Han Z F 2012 Chin. Phys. B 21 060202
[12] Li Y, Zhao L 2012 arXiv:1201.1196v3 [quant-ph]
[13] He Y C, Yang L, Wang X M 2001 J. China Institute Commun. 22 99 (in Chinese) [贺玉成, 杨莉, 王新梅 2001 通信学报 22 99]
[14] Frey B J, MacKay D J C 1997 Proceedings of 35th Allerton Conference on Communication, Control and Computing Champaign Urbana, USA 29 September–1 October, 1997 p1
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[1] Gisin N, Ribordy G, Wolfgang T, Zbinden H 2002 Rev. Mod. Phys. 74 145
[2] Zhao F, Li J L 2010 J. Optoelectronics·Laser 21 1383 (in Chinese) [赵峰, 李静玲 2010 光电子·激光 21 1383]
[3] Li S, Ma H Q, Wu L A, Zhai G J 2013 Acta Phys. Sin. 62 084214 (in Chinese) [李申, 马海强, 吴令安, 翟光杰 2013 62 084214]
[4] Yue X L, Wang J D, Wei Z J, Guo B H, Liu S H 2012 Acta Phys. Sin. 61 184215 (in Chinese) [岳孝林, 王金东, 魏正军, 郭邦红, 刘颂豪 2012 61 184215]
[5] Jiao R Z, Tang S J, Zhang C 2012 Acta Phys. Sin. 61 050302 (in Chinese) [焦荣珍, 唐少杰, 张弨 2012 61 050302]
[6] Bennett C, Bessette F, Brassard G, Salvail L, Smolin J 1992 J. Cryptol. 5 3
[7] Brassard G, Salvail L 1994 Advances in Cryptology–EUROCRYPT ’93 Norway, May 23-27, 1993 p410
[8] Buttler W T, Lamoreaux S K, Torgerson J R, Nickel G H, Donahue C H, Peterson C G 2003 Phys. Rev. A 67 052303
[9] Biham E, Boyer M, Boykin P, Mor T, Roychowdhury V 2006 J. Cryptol. 19 381
[10] Mayers D 2011 J. ACM 48 351
[11] Liu D, Yin Z Q, Wang S, Wang F M, Chen W, Han Z F 2012 Chin. Phys. B 21 060202
[12] Li Y, Zhao L 2012 arXiv:1201.1196v3 [quant-ph]
[13] He Y C, Yang L, Wang X M 2001 J. China Institute Commun. 22 99 (in Chinese) [贺玉成, 杨莉, 王新梅 2001 通信学报 22 99]
[14] Frey B J, MacKay D J C 1997 Proceedings of 35th Allerton Conference on Communication, Control and Computing Champaign Urbana, USA 29 September–1 October, 1997 p1
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