信息因果性作为界定量子关联集合的工具
Information causality as a tool for bounding the set of quantum correlations
AI总结：
本文提出从信息因果性原理导出多项式不等式的新技术，以界定任意二分贝尔场景中的物理关联集合，并推导出约束二元结果贝尔场景的非平凡不等式族，同时改进原理表述以获得超越Uffink不等式的更紧约束。
摘要：
信息因果性最初被提出作为一个物理原理，旨在推导量子力学对贝尔实验中观察到的关联类型的预测。在同一项工作中，信息因果性被著名地证明蕴含Uffink不等式，该不等式逼近量子关联集合，并重新推导了Clauser-Horne-Shimony-Holt不等式的Tsirelson界。由于从信息因果性原理推导其对非局域关联集合的影响存在困难，这一结果仅得到了有限的推广。在本文中，我们提出了一种简单技术，用于从信息因果性获得界定任何二分贝尔场景中物理关联集合的多项式不等式。这一结果使信息因果性成为逼近量子关联集合的有效工具。为演示我们的方法，我们推导了一族不等式，这些不等式在具有二元结果和相等测量设置数量的贝尔场景中非平凡地约束了非局域关联集合。最后，我们提出了信息因果性原理的一个改进表述，并为最简单的贝尔场景获得了更紧的约束，该约束超越了Uffink不等式，并恢复了量子集合边界的一部分。
英文摘要：
Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in the Bell experiment. In the same work, information causality was famously shown to imply the Uffink inequality that approximates the set of quantum correlations and rederives Tsirelson's bound of the Clauser-Horne-Shimony-Holt inequality. This result found limited generalizations due to the difficulty of deducing implications of the information causality principle on the set of nonlocal correlations. In this paper, we present a simple technique for obtaining polynomial inequalities from information causality bounding the set of physical correlations in any bipartite Bell scenario. This result makes information causality an efficient tool for approximating the set of quantum correlations. To demonstrate our method, we derive a family of inequalities which non-trivially constrains the set of nonlocal correlations in Bell scenarios with binary outcomes and equal number of measurement settings. Finally, we propose an improved statement of the information causality principle and obtain a tighter constraint for the simplest Bell scenario, that goes beyond the Uffink inequality and recovers a part of the boundary of the quantum set.
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