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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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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