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On safe post-selection for Bell tests with ideal detectors: Causal diagram approach
Quantum ( IF 5.1 ) Pub Date : 2021-11-11 , DOI: 10.22331/q-2021-11-11-575
Pawel Blasiak 1 , Ewa Borsuk 1 , Marcin Markiewicz 2
Affiliation  

Reasoning about Bell nonlocality from the correlations observed in post-selected data is always a matter of concern. This is because conditioning on the outcomes is a source of non-causal correlations, known as a $\textit{selection bias}$, rising doubts whether the conclusion concerns the actual causal process or maybe it is just an effect of processing the data. Yet, even in the idealised case without detection inefficiencies, post-selection is an integral part of experimental designs, not least because it is a part of the entanglement generation process itself. In this paper we discuss a broad class of scenarios with post-selection on multiple spatially distributed outcomes. A simple criterion is worked out, called the $\textit{all-but-one}$ principle, showing when the conclusions about nonlocality from breaking Bell inequalities with post-selected data remain in force. Generality of this result, attained by adopting the high-level diagrammatic tools of causal inference, provides safe grounds for systematic reasoning based on the standard form of multipartite Bell inequalities in a wide array of entanglement generation schemes, without worrying about the dangers of selection bias. In particular, it can be applied to post-selection defined by single-particle events in each detection chanel when the number of particles in the system is conserved.

中文翻译:

使用理想检测器进行贝尔测试的安全后选择:因果图方法

从后选择数据中观察到的相关性推理贝尔非局域性始终是一个值得关注的问题。这是因为对结果的调节是非因果相关性的来源,称为 $\textit{selection bias}$,越来越怀疑结论是否与实际因果过程有关,或者它只是处理数据的结果。然而,即使在没有检测效率低下的理想情况下,后选择也是实验设计的一个组成部分,尤其是因为它是纠缠生成过程本身的一部分。在本文中,我们讨论了一系列具有对多个空间分布结果进行后选择的场景。制定了一个简单的标准,称为 $\textit{all-but-one}$ 原则,显示当使用后选择数据打破贝尔不等式时关于非局域性的结论仍然有效。通过采用因果推理的高级图解工具获得的这一结果的普遍性,为基于多种纠缠生成方案中的多部分贝尔不等式的标准形式的系统推理提供了安全的基础,而无需担心选择偏差的危险. 特别是,当系统中的粒子数守恒时,它可以应用于由每个检测通道中的单粒子事件定义的后选择。在各种纠缠生成方案中,基于多部分贝尔不等式的标准形式,为系统推理提供了安全的基础,而无需担心选择偏差的危险。特别是,当系统中的粒子数守恒时,它可以应用于由每个检测通道中的单粒子事件定义的后选择。在各种纠缠生成方案中,基于多部分贝尔不等式的标准形式,为系统推理提供了安全的基础,而无需担心选择偏差的危险。特别是,当系统中的粒子数守恒时,它可以应用于由每个检测通道中的单粒子事件定义的后选择。
更新日期:2021-11-12
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