McDiarmid不等式在短密钥长诱骗态量子密钥分发中的应用
Application Of McDiarmid Inequality In Finite-Key-Length Decoy-State Quantum Key Distribution
摘要：
在实际的诱骗态量子密钥分发中，原始密钥长度是有限的。因此，由于有限的样本大小，估计的单光子产额和单光子错误率与它们各自的真实值的偏差可以严重降低可证明安全的密钥速率$R$。当前获得$R$下界的方法遵循一条间接路径，即首先以所使用的诱饵类型为条件来界定产量和错误率。然后使用这些边界来推导单光子产率和错误率，其进而用于计算密钥速率的下限$R$。这里我展示了如何通过统计学中的McDiarmid不等式直接计算$R$的下界。当原始密钥长度为$\approx 10^5$到$10^6$时，该方法将现实量子信道的可证明安全密钥速率提高了至少30%。更重要的是，这是通过纯理论分析实现的，而不改变实验装置或后处理方法。在更广泛的背景下，这项工作引入了强大的浓度不等式统计技术，以解决物理问题超出了简单的统计数据分析。
英文摘要：
In practical decoy-state quantum key distribution, the raw key length is finite. Thus, deviation of the estimated single photon yield and single photon error rate from their respective true values due to finite sample size can seriously lower the provably secure key rate $R$. Current method to obtain a lower bound of $R$ follows an indirect path by first bounding the yields and error rates both conditioned on the type of decoy used. These bounds are then used to deduce the single photon yield and error rate, which in turn are used to calculate a lower bound of the key rate $R$. Here I show how to directly compute a lower bound of $R$ via McDiarmid inequality in statistics. This method increases the provably secure key rate of realistic quantum channels by at least 30% when the raw key length is $\approx 10^5$ to $10^6$. More importantly, this is achieved by pure theoretical analysis without altering the experimental setup or the post-processing method. In a boarder context, this work introduces powerful concentration inequality techniques in statistics to tackle physics problem beyond straightforward statistical data analysis.
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