The causal modelling of Bell experiments relies on three fundamental assumptions: locality, freedom of choice and arrow-of-time. It turns out that nature violates Bell inequalities, which implies the failure of at least one of those assumptions. Since rejecting any of them, even partially, is sufficient to explain the observed correlations, it is natural to inquire about the cost in each case. This paper builds upon the findings in Blasiak et al. 2021 Proc. Natl Acad. Sci. USA 118 , e2020569118 ( doi:10.1073/pnas.2020569118 ) showing the equivalence between the locality and free choice assumptions. Here, we include retrocausal models to complete the picture of causal explanations of the observed correlations. Furthermore, we refine the discussion by considering more challenging causal scenarios which allow only single-arrow type violations of a given assumption. The figure of merit chosen for the comparison of the causal cost is defined as the minimal frequency of violation of the respective assumption required for a simulation of the observed experimental statistics. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

中文翻译：

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比较贝尔实验中违反因果假设的成本：局部性、自由选择和时间箭头

贝尔实验的因果模型依赖于三个基本假设：局部性、选择自由度和时间箭头。事实证明，自然违反了贝尔不等式，这意味着至少其中一个假设不成立。由于拒绝其中任何一个，即使是部分拒绝，都足以解释观察到的相关性，因此很自然地要询问每种情况的成本。本文基于 Blasiak 的研究结果等人。2021年过程。国家科学院。科学。美国 118, e2020569118 (doi:10.1073/pnas.2020569118）显示局部性和自由选择假设之间的等价性。在这里，我们包括逆因果模型来完成观察到的相关性的因果解释。此外，我们通过考虑更具挑战性的因果场景来完善讨论，这些场景仅允许单箭头类型违反给定的假设。为比较因果成本而选择的品质因数被定义为模拟观察到的实验统计数据所需的相应假设的最小违反频率。本文是“量子背景、因果关系和选择自由”主题的一部分。