Zhang Xiaoxu, Wang Yang, Jiang Musheng, Lu Yifei, Li Hongwei, Zhou Chun, Bao Wansu
Henan Key Laboratory of Quantum Information and Cryptography, SSF IEU, Zhengzhou 450001, China.
Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China.
Entropy (Basel). 2021 Apr 23;23(5):508. doi: 10.3390/e23050508.
The twin-field quantum key distribution (TF-QKD) protocol and its variations have been proposed to overcome the linear Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound. One variation called phase-matching QKD (PM-QKD) protocol employs discrete phase randomization and the phase post-compensation technique to improve the key rate quadratically. However, the discrete phase randomization opens a loophole to threaten the actual security. In this paper, we first introduce the unambiguous state discrimination (USD) measurement and the photon-number-splitting (PNS) attack against PM-QKD with imperfect phase randomization. Then, we prove the rigorous security of decoy state PM-QKD with discrete phase randomization. Simulation results show that, considering the intrinsic bit error rate and sifting factor, there is an optimal discrete phase randomization value to guarantee security and performance. Furthermore, as the number of discrete phase randomization increases, the key rate of adopting vacuum and one decoy state approaches infinite decoy states, the key rate between discrete phase randomization and continuous phase randomization is almost the same.
为克服线性皮兰多拉 - 劳伦扎 - 奥塔维亚尼 - 班奇（PLOB）界，人们提出了双场量子密钥分发（TF - QKD）协议及其变体。一种称为相位匹配量子密钥分发（PM - QKD）协议的变体采用离散相位随机化和相位后补偿技术，将密钥率提高了二次方。然而，离散相位随机化打开了一个漏洞，威胁到实际安全性。在本文中，我们首先介绍了针对具有不完美相位随机化的PM - QKD的无歧义态判别（USD）测量和光子数分裂（PNS）攻击。然后，我们证明了具有离散相位随机化的诱饵态PM - QKD的严格安全性。仿真结果表明，考虑到固有误码率和筛选因子，存在一个最优的离散相位随机化值来保证安全性和性能。此外，随着离散相位随机化数量的增加，采用真空和一个诱饵态的密钥率接近无限诱饵态，离散相位随机化和连续相位随机化之间的密钥率几乎相同。
