A necessary condition for the probabilities of a set of events to exhibit Bell non-locality or Kochen–Specker contextuality is that the graph of exclusivity of the events contains induced odd cycles with five or more vertices, called odd holes, or their complements, called odd antiholes. From this perspective, events whose graph of exclusivity are odd holes or antiholes are the building blocks of contextuality. For any odd hole or antihole, any assignment of probabilities allowed by quantum theory can be achieved in specific contextuality scenarios. However, here we prove that, for any odd hole, the probabilities that attain the quantum maxima cannot be achieved in Bell scenarios. We also prove it for the simplest odd antiholes. This leads us to the conjecture that the quantum maxima for any of the building blocks cannot be achieved in Bell scenarios. This result sheds light on why the problem of whether a probability assignment is quantum is decidable, while whether a probability assignment within a given Bell scenario is quantum is, in general, undecidable. This also helps to understand why identifying principles for quantum correlations is simpler when we start by identifying principles for quantum sets of probabilities defined with no reference to specific scenarios. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

中文翻译：

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在贝尔场景中，排他性基本图的量子极大值是无法达到的

一组事件展现贝尔非局域性或 Kochen-Specker 上下文性的概率的必要条件是，事件的排他性图包含具有五个或更多顶点的诱导奇循环，称为奇洞，或其补集，称为奇怪的反洞。从这个角度来看，排他性图表是奇怪漏洞或反漏洞的事件是上下文的基石。对于任何奇洞或反洞，量子理论允许的任何概率分配都可以在特定的上下文场景中实现。然而，在这里我们证明，对于任何奇孔，达到量子最大值的概率在贝尔场景中无法实现。我们还针对最简单的奇反洞证明了这一点。这导致我们推测任何构建块的量子最大值都无法在贝尔场景中实现。这个结果揭示了为什么概率分配是否是量子的问题是可判定的，而给定贝尔场景中的概率分配是否是量子的问题通常是不可判定的。这也有助于理解为什么当我们从识别不参考特定场景而定义的量子概率集的原理开始时，识别量子相关性的原理会更简单。本文是“量子背景、因果关系和选择自由”主题的一部分。