发表机构
Tel-Hai University of Kiryat Shmona in the Galilee; MIGAL Galilee Research Institute（加利利基里亚特希莫纳泰尔海大学; MIGAL加利利研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究2×3魔矩形这一非局部游戏，证明其量子值为(1+√(2/3))/2，分类最优策略，还关联了量子随机存取码的相关性质。
AI 中文摘要
2×3魔矩形是一种非局部游戏，其中两名玩家需在满足不相容奇偶性约束的条件下匹配条目。我们证明其量子值为(1+√(2/3))/2，并在任意有限局域维度（允许一般测量）下对所有最优策略进行分类。每一种最优策略都包含一对四维系统的最大纠缠态，在局域等距变换和辅助系统的范围内，局域态支撑上的测量是固定的。该达到构造此前已从量子随机存取码中为人所知。一个精确的平方和恒等式给出了上界，其等式关系确定了分类所需的测量代数。该魔矩形决定了在拥有量子侧信息的对手能完美预测艾丽丝第一行的情况下，与该情况兼容的最大魔方格得分。我们对所有达到该得分且满足完美预测的有限维策略进行分类，并表明最佳兼容猜测概率的1减去该概率，在得分超出该值时与得分超出量呈线性阶关系。同一刚性定理还对所有隐藏完整输入奇偶性的最优三位随机存取码进行了分类。
英文摘要
The $2\times3$ magic rectangle is a nonlocal game in which two players match entries subject to incompatible parity constraints. We prove that its quantum value is $(1+\sqrt{2/3})/2$ and classify all optimal strategies in arbitrary finite local dimensions, allowing general measurements. Every optimal strategy contains a maximally entangled pair of four-dimensional systems, with fixed measurements on the local state supports up to local isometries and ancillary systems. The attaining construction was previously known from quantum random access codes. An exact sum-of-squares identity gives the upper bound, and its equality relations determine the measurement algebra needed for the classification. The rectangle determines the largest magic-square score compatible with perfect prediction of Alice's first row by an adversary with quantum side information. We classify all finite-dimensional strategies attaining this score with perfect prediction and show that one minus the best compatible guessing probability has linear order in the score excess above it. The same rigidity theorem classifies all optimal three-bit random access codes that hide the full input parity.
Comments23 pages
