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测量设备无关量子密钥分发系统能够抵御任何针对单光子探测器边信道的攻击, 进一步结合诱惑态的方案, 可以同时规避准单光子源引起的实际安全漏洞. 测量设备无关量子密钥分发系统中, 非对称传输、分束器的不对称以及各个单光子探测器存在实际参数差异等光学系统的具体实现特征会对系统误码率和成码率等性能产生一定的影响. 本文针对采用弱相干光源的测量设备无关量子密钥分发系统, 引入单光子探测器品质因子的实验参数(暗计数与探测效率的比值), 通过量子化描述, 理论推导并模拟了误码率与单光子探测器品质因子、分束器反射率以及通信双方弱相干光源平均光子数之间的关系. 结果表明: 在X基偏振编码 和相位编码系统中, 当分束器的反射率趋近于0.5时, 误码率取最小值; 在偏振编码和相位编码系统中, 误码率随着单光子探测器品质因子的增大而增大; 在Z基偏振编码系统中, 误码率随分束器的反射率的变化会呈现较小的波动, 当分束器的反射率为0.5时, 若通信双方采用的平均光子数相差较大, 则误码率取最大值; 分束器的反射率和平均光子数对误码率的影响在Z基情况下不能等同, 但是对于X基编码和相位编码却能等同.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.
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Keywords:
- quantum key distribution /
- measurement-device-independent /
- quantum bit error rate /
- beam splitter
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[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
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