Chen Ziyang, Zhang Yichen, Wang Xiangyu, Yu Song, Guo Hong
State Key Laboratory of Advanced Optical Communication, Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China.
State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Entropy (Basel). 2019 Jul 2;21(7):652. doi: 10.3390/e21070652.
The entropic uncertainty relation (EUR) is of significant importance in the security proof of continuous-variable quantum key distribution under coherent attacks. The parameter estimation in the EUR method contains the estimation of the covariance matrix (CM), as well as the max-entropy. The discussions in previous works have not involved the effect of finite-size on estimating the CM, which will further affect the estimation of leakage information. In this work, we address this issue by adapting the parameter estimation technique to the EUR analysis method under composable security frameworks. We also use the double-data modulation method to improve the parameter estimation step, where all the states can be exploited for both parameter estimation and key generation; thus, the statistical fluctuation of estimating the max-entropy disappears. The result shows that the adapted method can effectively estimate parameters in EUR analysis. Moreover, the double-data modulation method can, to a large extent, save the key consumption, which further improves the performance in practical implementations of the EUR.
熵不确定关系（EUR）在相干攻击下连续变量量子密钥分发的安全性证明中具有重要意义。EUR方法中的参数估计包括协方差矩阵（CM）的估计以及最大熵的估计。先前工作中的讨论未涉及有限尺寸对CM估计的影响，而这会进一步影响泄漏信息的估计。在这项工作中，我们通过在可组合安全框架下将参数估计技术应用于EUR分析方法来解决这个问题。我们还使用双数据调制方法来改进参数估计步骤，在此方法中所有状态都可用于参数估计和密钥生成；因此，估计最大熵时的统计波动消失了。结果表明，改进后的方法能够有效地在EUR分析中估计参数。此外，双数据调制方法在很大程度上可以节省密钥消耗，这进一步提高了EUR在实际应用中的性能。
