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).

References

[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 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 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 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 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 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 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

[1]	Zhou Jiang-Ping, Zhou Yuan-Yuan, Zhou Xue-Jun. Improved parameter optimization method for measurement device independent protocol. Acta Physica Sinica, 2023, 72(12): 120303. doi: 10.7498/aps.72.20230179
[2]	Zhou Yang, Ma Xiao, Zhou Xing-Yu, Zhang Chun-Hui, Wang Qin. Study of practical state-preparation error tolerant reference-frame-independent quantum key distribution protocol. Acta Physica Sinica, 2023, 72(24): 240301. doi: 10.7498/aps.72.20231144
[3]	Liu Tian-Le, Xu Xiao, Fu Bo-Wei, Xu Jia-Xin, Liu Jing-Yang, Zhou Xing-Yu, Wang Qin. Regression-decision-tree based parameter optimization of measurement-device-independent quantum key distribution. Acta Physica Sinica, 2023, 72(11): 110304. doi: 10.7498/aps.72.20230160
[4]	Ke Hang, Li Pei-Li, Shi Wei-Hua. Two-dimensional photonic crystal waveguide 1×5 beam splitter reversely designed by downhill-simplex algorithm. Acta Physica Sinica, 2022, 71(14): 144204. doi: 10.7498/aps.71.20220328
[5]	Du Cong, Wang Jin-Dong, Qin Xiao-Juan, Wei Zheng-Jun, Yu Ya-Fei, Zhang Zhi-Ming. A simple protocol for measuring device independent quantum key distribution based on hybrid encoding. Acta Physica Sinica, 2020, 69(19): 190301. doi: 10.7498/aps.69.20200162
[6]	He Feng-Tao, Du Ying, Zhang Jian-Lei, Fang Wei, Li Bi-Li, Zhu Yun-Zhou. Bit error rate of pulse position modulation wireless optical communication in gamma-gamma oceanic anisotropic turbulence. Acta Physica Sinica, 2019, 68(16): 164206. doi: 10.7498/aps.68.20190452
[7]	Gu Wen-Yuan, Zhao Shang-Hong, Dong Chen, Wang Xing-Yu, Yang Ding. Reference-frame-independent measurement-device-independent quantum key distribution under reference frame fluctuation. Acta Physica Sinica, 2019, 68(24): 240301. doi: 10.7498/aps.68.20191364
[8]	Ma Jing, Liu Dong-Dong, Wang Ji-Cheng, Feng Yan. Anisotropic polarization beam splitter based on metal slit array. Acta Physica Sinica, 2018, 67(9): 094102. doi: 10.7498/aps.67.20172292
[9]	Yan Xia-Chao, Zhu Jiang, Zhang La-Bao, Xing Qiang-Lin, Chen Ya-Jun, Zhu Hong-Quan, Li Jian-Ting, Kang Lin, Chen Jian, Wu Pei-Heng. Model of bit error rate for laser communication based on superconducting nanowire single photon detector. Acta Physica Sinica, 2017, 66(19): 198501. doi: 10.7498/aps.66.198501
[10]	Sun Wei, Yin Hua-Lei, Sun Xiang-Xiang, Chen Teng-Yun. Nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions. Acta Physica Sinica, 2016, 65(8): 080301. doi: 10.7498/aps.65.080301
[11]	Wang Lü-Qiang, Su Tong, Zhao Bao-Sheng, Sheng Li-Zhi, Liu Yong-An, Liu Duo. Bit error rate analysis of X-ray communication system. Acta Physica Sinica, 2015, 64(12): 120701. doi: 10.7498/aps.64.120701
[12]	Du Ya-Nan, Xie Wen-Zhong, Jin Xuan, Wang Jin-Dong, Wei Zheng-Jun, Qin Xiao-Juan, Zhao Feng, Zhang Zhi-Ming. Analysis on quantum bit error rate in measurement-device-independent quantum key distribution using weak coherent states. Acta Physica Sinica, 2015, 64(11): 110301. doi: 10.7498/aps.64.110301
[13]	Zhou Fei, Yong Hai-Lin, Li Dong-Dong, Yin Juan, Ren Ji-Gang, Peng Cheng-Zhi. Study on quantum key distribution between different media. Acta Physica Sinica, 2014, 63(14): 140303. doi: 10.7498/aps.63.140303
[14]	Lü Jin-Guang, Liang Jing-Qiu, Liang Zhong-Zhu. Study on chromatic dispersion of beam splitter in spatially modulated Fourier transform spectrometer. Acta Physica Sinica, 2012, 61(14): 140702. doi: 10.7498/aps.61.140702
[15]	Tong Xing, Han Kui, Shen Xiao-Peng, Wu Qiong-Hua, Zhou Fei, Ge Yang, Hu Xiao-Juan. Equal intensity polarization-independent beam splitter based on photonic crystal self-collimation ring resonator. Acta Physica Sinica, 2011, 60(6): 064217. doi: 10.7498/aps.60.064217
[16]	Wei Zheng-Jun, Wan Wei, Wang Jin-Dong, Liao Chang-Jun, Liu Song-Hao. A new method to acquire the half-wave voltage by the quantum bit error rate in the deterministic quantum key distribution system. Acta Physica Sinica, 2011, 60(9): 094216. doi: 10.7498/aps.60.094216.1
[17]	Wang Jin-Dong, Wei Zheng-Jun, Zhang Hui, Zhang Hua-Ni, Chen Shuai, Qin Xiao-Juan, Guo Jian-Ping, Liao Chang-Jun, Liu Song-Hao. The influence of the time delay through long trunk fiber on the phase-coding quantum key distribution system. Acta Physica Sinica, 2010, 59(8): 5514-5522. doi: 10.7498/aps.59.5514
[18]	Mi Jing-Long, Wang Fa-Qiang, Lin Qing-Qun, Liang Rui-Sheng, Liu Song-Hao. Decoy state quantum key distribution with dual detectors heralded single photon source. Acta Physica Sinica, 2008, 57(2): 678-684. doi: 10.7498/aps.57.678
[19]	Chen Jie, Li Yao, Wu Guang, Zeng He-Ping. Stable quantum key distribution with polarization control. Acta Physica Sinica, 2007, 56(9): 5243-5247. doi: 10.7498/aps.56.5243
[20]	Ma Hai-Qiang, Li Ya-Ling, Zhao Huan, Wu Ling-An. A quantum key distribution system based on two polarization beam splitters. Acta Physica Sinica, 2005, 54(11): 5014-5017. doi: 10.7498/aps.54.5014

Catalog

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

Metrics

Abstract views: 7558
PDF Downloads: 383
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板