桥接资源理论与量子密钥分发：几何分析与统计检验
Bridging Resource Theory and Quantum Key Distribution: Geometric Analysis and Statistical Testing
AI总结：
本文将资源理论引入网络场景下的 QKD 协议，利用因果结构 $P3$ 对非凸多胞体进行几何分析，并提出统计检验方法度量行为间距离，从而把行为偏离与量子资源质量及残留非经典性直接关联。
AI中文摘要：
区分量子关联与经典关联具有极其重要的意义。Bell 多胞体已被确立为一种基本工具。在本文中，我们通过将资源理论应用于网络场景下的量子密钥分发（QKD）协议，拓展了这一研究方向。为此，我们考虑能够描述该协议的因果结构 $P3$，并致力于开发有用的统计检验方法来评估该结构。更具体地说，我们的目标有两点：首先，利用 QKD 协议的底层因果结构，对所得到的非凸多胞体进行几何分析，重点关注经典行为。其次，在该框架内设计一种检验方法，用于评估所生成多胞体内任意两种行为之间的距离。这一方法提供了一个独特的视角，将行为对预期结果的偏离直接与量子资源的质量或协议执行中残留的非经典性联系起来。
英文摘要：
Discerning between quantum and classical correlations is of great importance. Bell polytopes are well established as a fundamental tool. In this paper, we extend this line of inquiry by applying resource theory within the context of Network scenarios, to a Quantum Key Distribution (QKD) protocol. To achieve this, we consider the causal structure $P3$ that can describe the protocol, and we aim to develop useful statistical tests to assess it. More concretely, our objectives are twofold: firstly, to utilise the underlying causal structure of the QKD protocol to obtain a geometrical analysis of the resulting non-convex polytope, with a focus on the classical behaviours. Second, we devise a test within this framework to evaluate the distance between any two behaviours within the generated polytope. This approach offers a unique perspective, linking deviations from expected behaviour directly to the quality of the quantum resource or the residual nonclassicality in protocol execution.
