论文标题
网络非局部性通过令牌计数和颜色匹配的刚性
Network Nonlocality via Rigidity of Token-Counting and Color-Matching
论文作者
论文摘要
网络非局部性是对网络中共享的几个独立纠缠状态创建的网络非局部相关性的研究。在本文中，我们提供了前两种通用策略，以在没有输入的大量网络中产生非局部相关性。在第一个称为令牌计数（TC）的第一个中，每个源分布固定的令牌，每个方都计算接收的令牌的数量。在第二个称为颜色匹配（cm）的第二个中，每个源采用颜色和一个派对检查相邻源的颜色是否匹配。使用图理论工具和Finner的不平等，我们表明TC和CM分布在广泛的网络中是刚性的，这意味着基本上存在一种模拟此类相关性的独特经典策略。使用这种刚性特性，我们表明某些量子TC和CM策略产生了无法产生经典性的相关性。这使我们提出了几个没有输入的网络非局部性示例。这些示例涉及在整个网络中创造一致性，我们声称这是网络非局部性的真实形式的指纹。这项工作扩展了更紧凑的并行工作[通用网络的非局部性，arxiv：2011.02769]，并提供了所有必需的技术证明。
Network Nonlocality is the study of the Network Nonlocal correlations created by several independent entangled states shared in a network. In this paper, we provide the first two generic strategies to produce nonlocal correlations in large classes of networks without input. In the first one, called Token-Counting (TC), each source distributes a fixed number of tokens and each party counts the number of received tokens. In the second one, called Color-Matching (CM), each source takes a color and a party checks if the color of neighboring sources match. Using graph theoretic tools and Finner's inequality, we show that TC and CM distributions are rigid in wide classes of networks, meaning that there is essentially a unique classical strategy to simulate such correlations. Using this rigidity property, we show that certain quantum TC and CM strategies produce correlations that cannot be produced classicality. This leads us to several examples of Network Nonlocality without input. These examples involve creation of coherence throughout the whole network, which we claim to be a fingerprint of genuine forms of Network Nonlocality. This work extends a more compact parallel work [Nonlocality for Generic Networks, arXiv:2011.02769] on the same subject and provides all the required technical proofs.
