Jain Prabhav, Gachechiladze Mariami, Miklin Nikolai
Technical University of Darmstadt, Department of Computer Science, Darmstadt 64289, Germany.
Heinrich Heine University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany.
Phys Rev Lett. 2024 Oct 18;133(16):160201. doi: 10.1103/PhysRevLett.133.160201.
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 Letter, 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 nontrivially 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.
信息因果性最初是作为一种物理原理提出的，旨在推导量子力学对贝尔实验中所观察到的关联类型的预测。在同一篇论文中，信息因果性被证明蕴含乌菲克不等式，该不等式近似量子关联集并重新推导了克劳泽 - 霍恩 - 希莫尼 - 霍尔特不等式的齐雷尔森界。由于难以推导信息因果性原理对非局域关联集的影响，这一结果的推广受到限制。在本信函中，我们提出一种简单技术，可从信息因果性得出多项式不等式，这些不等式界定了任何二分贝尔场景中的物理关联集。这一结果使信息因果性成为近似量子关联集的有效工具。为演示我们的方法，我们推导了一族不等式，它们对具有二元结果且测量设置数量相等的贝尔场景中的非局域关联集进行了非平凡的约束。最后，我们提出信息因果性原理的一种改进表述，并对最简单的贝尔场景得到了一个比乌菲克不等式更严格的约束，该约束恢复了量子集边界的一部分。
