发表机构
University of Copenhagen（哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过构造带标志的魔方博弈，证明完美非局域性需要特定非最大纠缠态，并利用博弈到信道约化表明该纠缠在零误差通信中优于最大纠缠态。
AI 中文摘要
我们识别出一种结构机制，通过该机制，非局域博弈中的完美发挥需要并自测试一种特定的非最大纠缠态。为此，我们通过为标准魔方博弈增加一个额外的“标志”结果和每个玩家的两个额外问题，构建了一个带标志的魔方博弈。该博弈允许使用施密特系数与$(1,\sqrt{2},\sqrt{2},\sqrt{2},\sqrt{2})$成比例的状态的完美策略。我们给出了一个直接的代数证明，表明最大纠缠策略的获胜概率在任意维度下都严格小于一。此外，该博弈自测试这种状态，提供了一个两方伪心灵感应博弈的实例，该博弈认证了一种特定的非最大纠缠态。我们的构造说明了如何向刚性测量几何添加合适的约束以强制特定的施密特比率，并提供了一种基于其他刚性伪心灵感应博弈的模块化途径以进一步自测试。我们建立了一个通用的博弈到信道约化，将博弈模型中的分离转移到经典信道上的单发零误差通信。应用于带标志的魔方博弈，它产生了一个经典信道，在该信道上，纠缠允许单次使用零误差传输十条消息，而任何有限维最大纠缠资源最多允许九条。因此，最大纠缠态并非经典噪声信道上零误差通信的普遍最优纠缠资源。
英文摘要
We identify a structural mechanism by which perfect play in a nonlocal game requires and self-tests a specific non-maximally entangled state. To this end, we construct a Flagged Magic-Square game by extending the standard Magic-Square game with an additional ``flag'' outcome and two additional questions for each player. The game admits a perfect strategy using a state with Schmidt coefficients proportional to $(1,\sqrt{2},\sqrt{2},\sqrt{2},\sqrt{2})$. We give a direct algebraic proof that maximally entangled strategies have winning probability bounded away from one, independently of dimension. Moreover, the game self-tests this state, providing an example of a two-party pseudo-telepathy game that certifies a specific non-maximally entangled state. Our construction illustrates how adding suitable constraints to a rigid measurement geometry can enforce specific Schmidt ratios and provides a modular route to further self-tests based on other rigid pseudo-telepathy games. We establish a general game-to-channel reduction that transfers separations in the game model to one-shot zero-error communication over classical channels. Applied to the Flagged Magic-Square game, it yields a classical channel for which entanglement permits the zero-error transmission of ten messages in a single use, whereas any finite-dimensional maximally entangled resource permits at most nine. Thus, maximally entangled states are not a universally optimal entanglement resource for zero-error communication over classical noisy channels.
