基于四态协议的半量子密钥分发诱骗态模型的有限码长分析  

Finite-key analysis of decoy model semi-quantum key distribution based on four-state protocol

作　　者：詹绍康 王金东[1] 董双 黄偲颖 侯倾城 莫乃达 弥赏 向黎冰 赵天明 於亚飞[2] 魏正军[1] 张智明[2] Zhan Shao-Kang;Wang Jin-Dong;Dong Shuang;Huang Si-Ying;Hou Qing-Cheng;Mo Nai-Da;Mi Shang;Xiang Li-Bing;Zhao Tian-Ming;Yu Ya-Fei;Wei Zheng-Jun;Zhang Zhi-Ming(Guangdong Provincial Key Laboratory of Quantum Control Engineering and Materials,School of Information and Optoelectronic Science and Engineering,South China Normal University,Guangzhou 510006,China;Guangdong Provincial Key Laboratory of Micro-nanophotonic Functional Materials and Devices,School of Information and Optoelectronic Science and Engineering,South China Normal University,Guangzhou 510006,China)

机构地区：[1]华南师范大学信息光电子科技学院,广东省量子调控工程与材料重点实验室,广州510006 [2]华南师范大学信息光电子科技学院,广东省微纳光子功能材料与器件重点实验室,广州510006

出　　处：《物理学报》2023年第22期82-92,共11页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:62071186,61771205);广东省重点实验室基金(批准号:2020B1212060066)资助的课题。

摘　　要：半量子密钥分发允许一个全量子用户Alice和一个经典用户Bob共享一对由物理原理保障的安全密钥.在半量子密钥分发被提出的同时其鲁棒性获得了证明,随后半量子密钥分发系统的无条件安全性被理论验证.2021年基于镜像协议的半量子密钥分发系统的可行性被实验验证.然而,可行性实验系统仍旧采用强衰减的激光脉冲,已有文献证明,半量子密钥分发系统在受到光子数分裂攻击时仍旧面临密钥比特泄露的风险,因此,在密钥分发过程中引入诱骗态并且进行有限码长分析,可以进一步合理评估密钥分发的实际安全性.本文基于四态协议的半量子密钥分发系统,针对仅在发送端Alice处加入单诱骗态的模型,利用Hoeffding不等式进行了有限码长情况的安全密钥长度分析,进而求得安全密钥率公式,其数值模拟结果表明,当选择样本量大小为105时,能够在近距离情况下获得10-4bit/s安全密钥速率,与渐近情况下的安全密钥率相近,这对半量子密钥分发系统的实际应用具有非常重要的意义.Semi-quantum key distribution allows a full quantum user Alice and a classical user Bob to share a pair of security keys guaranteed by physical principles.Semi-quantum key distribution is proposed while verifying its robustness.Subsequently,its unconditional security of semi-quantum key distribution system is verified theoretically.In 2021,the feasibility of semi-quantum key distribution system based on mirror protocol was verified experimentally.However,the feasibility experimental system still uses the laser pulse with strong attenuation.It has been proved in the literature that the semi-quantum key distribution system still encounters the risk of secret key leakage under photon number splitting attack.Therefore,the actual security of key distribution can be further reasonably evaluated by introducing the temptation state and conducting the finite-key analysis in the key distribution process.In this work,for the model of adding one-decoy state only to Alice at the sending based on a four state semi-quantum key distribution system,the length of the security key in the case of finite-key is analyzed by using Hoeffding inequality,and then the formula of the security key rate is obtained.It is found in the numerical simulation that when the sample size is 10~5,the security key rate of 10~(-4),which is close to the security key rate of the asymptotic limits,can be obtained in the case of close range.It is very important for the practical application of semi-quantum key distribution system.

关 键 词：半量子密钥分发 诱骗态 Hoeffding不等式 有限码长 

分 类 号：O413[理学—理论物理] TN918[理学—物理]