In a Bell test, the set of observed probability distributions complying with the principle of local realism is fully characterized by Bell inequalities. Quantum theory allows for a violation of these inequalities, which is famously regarded as Bell nonlocality. However, finding the maximal degree of this violation is, in general, an undecidable problem. Consequently, no algorithm can be used to derive quantum analogs of Bell inequalities, which would characterize the set of probability distributions allowed by quantum theory. Here we present a family of inequalities, which approximate the set of quantum correlations in Bell scenarios where the number of settings or outcomes can be arbitrary. We derive these inequalities from the principle of Information Causality, and thus, we do not assume the formalism of quantum mechanics. Moreover, we identify a subspace in the correlation space for which the derived inequalities give the necessary and sufficient conditions for the principle of Macroscopic Locality. As a result, we show that in this subspace, the principle of Information Causality is strictly stronger than the principle of Macroscopic Locality.

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来自信息因果关系的量子贝尔不等式——对宏观局部性来说很紧

在贝尔检验中，观察到的符合局部现实主义原则的概率分布集完全由贝尔不等式表征。量子理论允许违反这些不等式，这被认为是著名的贝尔非定域性。然而，找到这种违反的最大程度通常是一个无法确定的问题。因此，没有算法可以用来推导贝尔不等式的量子模拟，这将表征量子理论允许的概率分布集。在这里，我们提出了一系列不等式，它们近似于贝尔场景中的一组量子相关性，其中设置或结果的数量可以是任意的。我们从信息因果关系原理推导出这些不等式，因此，我们不假设量子力学的形式主义。而且，我们确定了相关空间中的一个子空间，其中导出的不等式为宏观局部性原理提供了充分的必要条件。结果表明，在这个子空间中，信息因果性原理严格地强于宏观局部性原理。