Analysis on performance optimization in measurement-device-independent quantum key distribution using weak coherent states

Wu Cheng-Feng; Du Ya-Nan; Wang Jin-Dong; Wei Zheng-Jun; Qin Xiao-Juan; Zhao Feng; Zhang Zhi-Ming

doi:10.7498/aps.65.100302

Abstract

Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all detection side-channel attacks, thus when combined with the decoy-state method, it can avoid the actual security loophole caused by quasisingle- photon source simultaneously. A practical weak coherent source is used as a quasi-single-photon source in the current MDI-QKD experiments; it may contain percentage of vacuum-and multi-photon pulses. Moreover, in order to study how the performance of the threshold detector affects the quantum bit error rate (QBER), we introduce the quality factor (the ratio of the dark count rate to the detection efficiency) of the threshold detector. Here, through taking into account the weak coherent source, the quality factor of the threshold detector and the reflectivity of beam splitter, we deduce and evaluate the gain, the probability for successful Bell measurement, incorrect Bell measurement when Alice and Bob send pulses with different photon numbers which have a high probability to appear in weak coherent source, and then we obtain QBER in combination with the probabilities of different photon number states, besides, we also do some simulations. The simulations show how QBER varies with the reflectivity of beam splitter and the quality factor of the threshold detector when the average photon numbers per pulse from Alice and Bob are symmetric. Furthermore, the simulations show how QBER varies with the average photon number per pulse from Alice when average photon number per pulse from Bob is 0.1. Result shows that QBER is affected by the reflectivity of beam splitter, but QBER cannot reach the minimum value in Z basis encoding scheme when the average photon numbers per pulse from Alice and Bob are both 0.1 and the reflectivity of beam splitter is 0.5, which is different from X basis encoding and phase encoding. In addition, QBER increases with the increase of the quality factor of the threshold detector, which means that better performance of the threshold detector will reduce QBER. We show that QBER in Z basis encoding reaches the minimum value when reflectivity of beam splitter is 0.5 and there is large difference between in average photon number per pulse between two sides. In conclusion, for QBER, the effect from the reflectivity of beam splitter is equal to average photon numbers from the two arms only in X basis encoding and phase encoding. Our work will provide a reference for setting up a system with better performance.

Keywords:

Authors and contacts

1.
Laboratory of Nanophotonic Functional Materials and Devices (SIPSE), and Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China;
2.
Engineering Technology Department, Guangdong Polytechnic Institute, Guangzhou 510091, China;
3.
School of Physics and Telecommunication Engineering, Shaanxi University of Technology, Hanzhong 723000, China

Corresponding author: Wang Jin-Dong, wangjd@scnu.edu.cn

Funds: Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91121023), the National Natural Science Foundation of China (Grant Nos. 61378012, 11374107, 60978009, 61108039, 61401176, 61401262), the Natural Science Foundation of Guangdong Province, China (Grant Nos. 2014A030310205, 2015A030313388), the National Basic Research Program of China (Grant No. 2011CBA00200), and the Application-oriented Special Scientific Research Fund of Application Type of Guangdong Province, China (Grant No. 2015B010128012).

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[12]	Zhao Y, Fung C H F, Qi B, Chen C, Lo H K 2008 Phys. Rev. A 78 042333
[13]	Qi B, Fung C H F, Lo H K, Ma X 2007 Quantum Inf. Comput. 7 073
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[21]	Zhou C, Bao W S, Chen W, Li H W, Yin Z Q, Wang Y, Han Z F 2013 Phys. Rev. A 88 052333
[22]	Wang Y, Bao W S, Li H W, Zhou C, Li Y 2014 Chin. Phys. B 23 080303
[23]	Ma X F, Fung C H F, Razavi M 2012 Phys. Rev. A 86 052305
[24]	Tang Z Y, Liao Z F, Xu F H, Qi B, Qian L, Lo H K 2014 Phys. Rev. Lett. 112 190503
[25]	Tang Y L, Yin H L, Chen S J, Liu Y, Zhang W J, Jiang X, Zhang L, Wang J, You L X, Guan J Y, Yang D X, Wang Z, Liang H, Zhang Z, Zhou N, Ma X F, Chen T Y, Zhang Q, Pan J W 2014 Phys. Rev. Lett. 114 069901
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[27]	Dong C, Zhao S H, Zhang N, Dong Y, Zhao W H, Liu Y 2014 Acta Phys. Sin. 63 200304 (in Chinese) [东晨, 赵尚弘, 张宁, 董毅, 赵卫虎, 刘韵 2014 物理学报 63 200304]
[28]	Liu Y, Chen T Y, Wang L J, Liang H, Shentu G L, Wang J, Cui K, Yin H L, Liu N L, Li L, Ma X F, Pelc J S, Fejer M M, Peng C Z, Zhang Q, Pan J W 2013 Phys. Rev. Lett. 111 130502
[29]	Sun S H, Gao M, Li C Y, Liang L M 2013 Phys. Rev. A 87 052329
[30]	Du Y N, Xie W Z, Jin X, Wang J D, Wei Z J, Qin X J, Zhao F, Zhang Z M 2015 Acta Phys. Sin. 64 110301 (in Chinese) [杜亚男, 解文钟, 金璇, 王金东, 魏正军, 秦晓娟, 赵峰, 张智明 2015 物理学报 64 110301]
[31]	Wang Q, Wang X B 2013 Phys. Rev. A 88 052332
[32]	Li M, Zhang C M, Yin Z Q, Chen W, Wang S, Guo G C, Han Z F 2014 Opt. Lett. 39 880

Cited By

[1]	Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145
[2]	Li M, Patcharapong T, Zhang C M, Yin Z Q, Chen W, Han Z F 2015 Chin. Phys. B 24 010302
[3]	Ma H Q, Wei K J, Yang J H, Li R X, Zhu W 2014 Chin. Phys. B 23 100307
[4]	Chen W F, Wei Z J, Guo L, Hou L Y, Wang G, Wang J D, Zhang Z M, Guo J P, Liu S H 2014 Chin. Phys. B 23 080304
[5]	Zhou Y Y, Zhou X J, Tian P G, Wang Y J 2013 Chin. Phys. B 22 010305
[6]	Zhou R R, Y L 2012 Chin. Phys. B 21 080301
[7]	Tang Y L, Yin H L, Chen S J, Liu Y, Zhang W J, Jiang X, Zhang L, Wang J, You L X, Guan J Y, Yang D X, Wang Z, Liang H, Zhang Z, Zhou N, Ma X F, Chen T Y, Zhang Q, Pan J W 2015 IEEE J. Select. Topics Quantum Electron. 21 6600407
[8]	Lo H K, Chau H F 1999 Science 283 2050
[9]	Shor P W, Preskill J 2000 Phys. Rev. Lett. 85 441
[10]	Mayers D 2001 J. ACM 48 351
[11]	Makarov V, Anisimov A, Skaar J 2006 Phys. Rev. A 74 022313
[12]	Zhao Y, Fung C H F, Qi B, Chen C, Lo H K 2008 Phys. Rev. A 78 042333
[13]	Qi B, Fung C H F, Lo H K, Ma X 2007 Quantum Inf. Comput. 7 073
[14]	Brassard G, Lutkenhaus N, Mor T, Sanders B C 2000 Phys. Rev. Lett. 85 1330
[15]	Sun S H, Liang L M 2012 Appl. Phys. Lett. 101 071107
[16]	Acn A, Brunner N, Gisin N, Massar S, Pironio S, Scarani V 2007 Phys. Rev. Lett. 98 230501
[17]	Gisin N, Pironio S, Sangouard N 2010 Phys. Rev. Lett. 105 070501
[18]	Lo H K, Curty M, Qi B 2012 Phys. Rev. Lett. 108 130503
[19]	Hwang W Y 2003 Phys. Rev. Lett. 91 057901
[20]	Ma X F, Razavi M 2012 Phys. Rev. A 86 062319
[21]	Zhou C, Bao W S, Chen W, Li H W, Yin Z Q, Wang Y, Han Z F 2013 Phys. Rev. A 88 052333
[22]	Wang Y, Bao W S, Li H W, Zhou C, Li Y 2014 Chin. Phys. B 23 080303
[23]	Ma X F, Fung C H F, Razavi M 2012 Phys. Rev. A 86 052305
[24]	Tang Z Y, Liao Z F, Xu F H, Qi B, Qian L, Lo H K 2014 Phys. Rev. Lett. 112 190503
[25]	Tang Y L, Yin H L, Chen S J, Liu Y, Zhang W J, Jiang X, Zhang L, Wang J, You L X, Guan J Y, Yang D X, Wang Z, Liang H, Zhang Z, Zhou N, Ma X F, Chen T Y, Zhang Q, Pan J W 2014 Phys. Rev. Lett. 114 069901
[26]	Sun Y, Zhao S H, Dong C 2015 Acta Phys. Sin. 64 140304 (in Chinese) [孙颖, 赵尚弘, 东晨 2015 物理学报 64 140304]
[27]	Dong C, Zhao S H, Zhang N, Dong Y, Zhao W H, Liu Y 2014 Acta Phys. Sin. 63 200304 (in Chinese) [东晨, 赵尚弘, 张宁, 董毅, 赵卫虎, 刘韵 2014 物理学报 63 200304]
[28]	Liu Y, Chen T Y, Wang L J, Liang H, Shentu G L, Wang J, Cui K, Yin H L, Liu N L, Li L, Ma X F, Pelc J S, Fejer M M, Peng C Z, Zhang Q, Pan J W 2013 Phys. Rev. Lett. 111 130502
[29]	Sun S H, Gao M, Li C Y, Liang L M 2013 Phys. Rev. A 87 052329
[30]	Du Y N, Xie W Z, Jin X, Wang J D, Wei Z J, Qin X J, Zhao F, Zhang Z M 2015 Acta Phys. Sin. 64 110301 (in Chinese) [杜亚男, 解文钟, 金璇, 王金东, 魏正军, 秦晓娟, 赵峰, 张智明 2015 物理学报 64 110301]
[31]	Wang Q, Wang X B 2013 Phys. Rev. A 88 052332
[32]	Li M, Zhang C M, Yin Z Q, Chen W, Wang S, Guo G C, Han Z F 2014 Opt. Lett. 39 880

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Vol. 65, Issue 10 - 2016-05-20

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