量子密钥分发的有限统计极限
Sharp finite statistics for quantum key distribution
AI总结：
本文针对量子密钥分发的随机抽样统计任务，提出了紧性优于传统Serfling尾界的替代方案，可降低QKD所需最小分组大小，其置信区间也适用于诱骗态QKD分析。
摘要：
量子密钥分发（QKD）的性能高度依赖统计推断。对于广泛类别的协议，核心统计任务是随机抽样问题，通常使用Serfling提出的超几何尾界处理。本文为该任务提供了量子密钥分发安全分析中前所未有的紧性替代解决方案，作为副产品，非同质伯努利参数平均值的置信区间也可推导，这些结果自然适用于诱骗态QKD的统计分析，且优于标准工具。最后，我们表明在大量参数范围内，无需使用尾界，因为超几何分布的累积质量函数可精确计算，这大幅降低了QKD所需的最小分组大小，并揭示了考虑中到大分组时分析界的紧性。
英文摘要：
The performance of quantum key distribution (QKD) heavily depends on statistical inference. For a broad class of protocols, the central statistical task is a random sampling problem, customarily addressed using a hypergeometric tail bound due to Serfling. Here, we provide an alternative solution for this task of unprecedented tightness among QKD security analyses. As a by-product, confidence intervals for the average of nonidentical Bernoulli parameters follow too. These naturally fit in statistical analyses of decoy-state QKD and also outperform standard tools. Last, we show that, in a vast parameter regime, the use of tail bounds is not enforced because the cumulative mass function of the hypergeometric distribution is accurately computable. This sharply decreases the minimum block sizes necessary for QKD, and reveals the tightness of our analytical bounds when moderate-to-large blocks are considered.
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