非完美探测效率对设备无关量子随机数扩展的影响  

On the Impact of Imperfect Detection Efficiency on Device Independent Quantum Random Number Expansion

作　　者：李超博 费洋扬 王洪[1,2] 高明[1,2] 马智[1,2] 

机构地区：[1]信息工程大学,郑州450002 [2]数学工程与先进计算国家重点实验室,郑州450002

出　　处：《密码学报》2015年第3期217-225,共9页Journal of Cryptologic Research

基　　金：国家高技术研究发展计划(863项目)(2011AA010803);国家自然科学基金项目(U1204602;61472446)

摘　　要：设备无关(Device Independent,简记为DI)量子随机数扩展方案中,在不需要考虑系统内部工作状态前提下,基于纠缠粒子的非局域特性可以证明随机性的存在.但在实际条件下的可行性受到探测效率等因素的限制.本文在CHSH不等式中引入探测效率参数,从两方面探究非完美探测效率对DI随机数扩展方案的影响,数值模拟出将未探测事件作为结果保留和随机赋值时非完美探测效率下小熵与CHSH违背值的定量关系.将未探测事件作为结果保留时,可得在相同CHSH值下较低的探测效率对应的实验中量子态和测量过程蕴含更多的随机性,而在相同的的实验环境下,探测效率的降低会使实验中输出序列小熵变小.将未探测事件随机赋值时,在相同的CHSH违背值下,伴随着探测效率的降低,小熵界逐渐变小.通过SDP优化算法可得此情形下进行DI随机数扩展的探测效率下界为91.1%.通过对非完美探测效率的量化分析,可得实际条件下更为准确的DI量子随机数扩展效率分析.In a Device Independent(Denoted as DI) quantum random number expansion protocol, the randomness can be proved by nonlocal correlations of entanglement particles without considering internal working conditions in the system. However, in real circumstances, its feasibility may be restricted by some factors such as detection efficiencies. This paper introduces the detection efficiency parameter to the CHSH inequality to discover the influence of imperfect detection efficiency on DI random number expansion in two different situations. We establish the relationship between CHSH violation and entropy under different detection efficiencies from two aspects that treating undetected events as a result or assigning undetected events randomly. When treating the no-detected events as a result, for the same CHSH value, we can determine that the corresponding experiment under lower detection efficiency contains more randomness from quantum state and measurements process. Meanwhile, in the same experimental environment, the entropy decreases with lower detection efficiencies. When assigning the no-detected events randomly, we can get the lower bound of detection efficiency for DI random number expansion to be 91.1% according to SDP. Therefore, we analysis the influence of imperfect detection efficiency which will further benefit to the increasing efficiency of device independent quantum random number expansion.

关 键 词：设备无关 随机数扩展 CHSH不等式 探测效率 

分 类 号：TN918.1[电子电信—通信与信息系统] O413[电子电信—信息与通信工程]