有限长度量子密钥的纠错误码率估计仿真分析

J4 ›› 2014, Vol. 31 ›› Issue (2): 167-172.

有限长度量子密钥的纠错误码率估计仿真分析

赵峰,井敏英,李静玲,张文丽

陕西理工学院物理与电信工程学院，陕西汉中，723000

收稿日期:2013-07-15 修回日期:2013-10-16 出版日期:2014-03-28 发布日期:2014-03-20
通讯作者: 赵峰（1979-）陕西安康人,博士,副教授,主要从事量子信息技术领域的研究。 E-mail:hfengzhao@126.com
作者简介:赵峰（1979-）陕西安康人,博士,副教授,主要从事量子信息技术领域的研究。E-mail:hfengzhao@126.com
基金资助:
教育部科学技术研究重点项目（212177 ）；陕西省科技厅自然基金项目（2011JQ1003）；陕西省教育厅科研专项（12JK0973）资助

Estimates for BER of error correcting on finite quantum key

ZHAO Feng, JING Min-ying, LI Jing-ling, ZHANG Wen-li

School of Physics and Telecommunication Engineering, Shaanxi University of Technology，Hanzhong 723000, China

Received:2013-07-15 Revised:2013-10-16 Published:2014-03-28 Online:2014-03-20

摘要/Abstract

摘要： 基于奇偶检错-汉明纠错算法的误码率后验分布参数，用仿真数据直接估计纠错后的误码率及其置信区间。实验利用了两个伪随机二进制序列替代原始量子密钥，长度为1.4×10-7，误码呈二项分布，通过奇偶检错后利用(7,4)汉明码对奇偶性不一致的码字进行纠错。实验结果表明：当初始误码率为3%时，通过一次检错、纠错，误码率降至2.47×10-3，置信度为95%的上限值为2.77×10-3；当初始误码率为0.1%时，通过一次纠错，误码率降至1.43×10-7，置信度为95%的上限值为10.54×10-7。该方法有效地估计了奇偶-汉明纠错码对有限长度原始量子密钥纠错后的误码率，为量子密钥分配后续处理提供了可靠的数据支持。

关键词: 量子光学, 误码率估计, 数据仿真, 后续数据处理；

Abstract: Based on the parameters of posterior distribution of BER (Bit Error Rate) regarding parity check-Hamming correction protocol,the BER and its confidence interval of the remaining quantum keys are directly estimated. In experiment,instead of the raw quantum keys,we use two pseudo-random binary sequences which have the length of 1.4×10-7 and the BER follow binomial distribution.The Error correction process utilizes the parity code and Hamming code for error detection and correction respectively.The experimental results showed that: when the initial bit error rate at 3% and 0.1%,by one time error detection and error correction, the BER falls to 2.47×10-3 and 1.43×10-7 respectively, when the confidence at 95%, the corresponding upper limit of BER at 2.77×10-3 and 10.57×10-7 respectively. These experimental results effectively assessed parity - Hamming error correction performance on the finite quantum keys,and provided reliable data for the post-processing in the quantum key distribution.

Key words: quantum optics, BER estimating, data simulation, data post-processing

中图分类号:

TN91

赵峰井敏英李静玲张文丽. 有限长度量子密钥的纠错误码率估计仿真分析[J]. J4, 2014, 31(2): 167-172.

ZHAO Feng, JING Min-ying, LI Jing-ling, ZHANG Wen-li. Estimates for BER of error correcting on finite quantum key[J]. J4, 2014, 31(2): 167-172.

参考文献

[1] W. K. Wootters, W. H. Zurek. A single quantum cannot be cloned[J].Nature(London),1982, 299(588):802-803.
[2] N. Gisin, G. Ribordy, T. Wolfgang, et al. Quantum cryptography[J]. Rev. Mod. Phys., 2002,74(1):145-195.
[3] D. Rosenberg, J. W. Harrington, P. R. Rice, et al. Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber[J]. Phys. Rev. Lett., 2007,98(1):010503.
[4] H. Takesue, S. W. Nam, Q. Zhang, et al. Quantum key distribution over 40 dB channel loss using super- conducting single photon detectors[J]. Nature Photonics, 2007,1:343.
[5] D. Stucki, N. Walenta, F. Vannel, et al. High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres[J]. New J. Phys., 2009,11(7):075003.
[6] J. F. Dynes, H. Takesue, Z. L. Yuan,et al. Efficient entanglement distribution over 200 kilometers[J]. Opt. Express, 2009, 17(14):11440.
[7] T. E. Chapuran, P. Toliver, N. A. Peters, et al. Optical networking for quantum key distribution and quantum communications[J]. N. J. Phys., 2009,11(10):105001.
[8] S. Wang, W. Chen, Z. Q. Yin, et al. Field test of wavelength-saving quantum key distribution network [J]. Opt. Lett.,2010,35(14):2454.
[9] T. Y. Chen, J. Wang, H. Liang, et al. Metropolitan all-pass and inter-city quantum communication network[J]. Opt. Express, 2010,18(26):27217.
[10] M. Sasaki, M. Fujiwara, H. Ishizuka, et al. Field test of quantum key distribution in the Tokyo QKD Network [J]. Opt. Express,2011,19(11):10387.
[11] Cao Dong, Song Yaoliang. Computationally secure bit commitment protocol based on quantum steganography[J]. Chinese Journal of Quantum Electronics(量子电子学报) ,2012, 29 (1): 63-68 (in Chinese)
[12] Zhao Long,Cao Zhenwen,Luo Rui,et al. Multi-signature scheme based on quantum properties[J].Chinese Journal of Quantum Electronics(量子电子学报),2012,29 (1): 69-73 (in Chinese)
[13] Jiang Jinya,Nie Min,Liu Xiaohui. Layered model of quantum signaling and realizable strategy of entanglement distribution layer function[J].Chinese Journal of Quantum Electronics(量子电子学报),2012,29 (5): 555-560 (in Chinese)
[14] Jiang Zhongsheng, Lu Hongjun,Xie Guangjun. Multidimensional controllable quantum superdense coding information transfer[J].Chinese Journal of Quantum Electronics(量子电子学报),2013,30 (4): 450-454 (in Chinese)
[15] Zhao Feng, Li Jingling. Analysis of the coefficient of QBER and it influence[J]. Journal of Optoelectronics?Laser(光电子.激光), 2010,21(9) :1383-1385 (in Chinese)
[16] Liu Linyao, Humengjun,Lu Hongjun,et al. Quantum key distribution based on arbitrary BELL state[J]. Journal of Optoelectronics?Laser(量子电子学报), 2013,30 (4): 439-444 (in Chinese)
[17] Kuritsyn K. Modification of error reconciliation scheme for quantum cryptography[C]. Proceedings of SPIE,2003, 5128:91-94.
[18] Buttler WT, Lamoreaux SK, Torgerson JR et al. Fast, efficient error reconciliation for quantum cryptography[J]. Phys.Rev.A ,2003,67(5):052303.
[19] Zhao Feng, Fu Mingxing, Wang Faqiang, et al. Error reconciliation for practical quantum cryptography[J]. Optik-International Journal for Light and Electron Optics,2007,118(10): 502-506
[20] H. F. Zhang, J. Wang, K. Cui, et al. A Real-Time QKD System Based on FPGA[J].J. Light. Tech.,2012,30(20): 3226-3234
[21] He Yucheng, Yang Li, Wang Xin-mei. Estamates for BER of error correcting codes in performance simulations[J]. Journal of China Institute of Communication(通信学报),2001,22(9):99-103 (in Chinese)
[22] B.J. Frey,D.J.C.MacKay.Trellis-Constrained Codes[C]. Proceedings of 35th Allerton Conference on communication,1997,1-10.