因果性的几何
The Geometry of Causality
AI总结：
本文提出统一的设备与理论无关的操作框架，通过定义causaltopes并利用线性规划计算因果分数与因果可分性，揭示了因果不可分性与非定域性及情境性之间的关联。
摘要：
我们提供了一个统一的操作框架，用于在完全与设备无关且与理论无关的设定下研究因果性、非定域性和情境性。我们针对任意的输入历史空间和任意的输入情境选择，定义了causaltopes（我们选择的“因果多面体”的混成词）。我们证明了causaltopes是通过用一组因果性方程切片更简单的条件概率分布多面体得到的，我们对此进行了完整刻画。我们提供了高效的线性规划，用于计算由任意给定子causaltope支持的经验模型的最大分量，以及相关的因果分数。我们引入了相对于任意因果约束的因果可分性概念。我们提供了高效的线性规划，用于计算经验模型的最大因果可分分量，从而计算其因果可分分数，即由某些子causaltopes共同支持的分量。我们研究了几种新示例的因果分数和因果可分性，包括具有纠缠或情境控制的一组量子开关。在此过程中，我们证明了“因果情境性”的存在，这是一种因果不可分性与非定域性和情境性明显相关，甚至直接由其蕴含的现象。
英文摘要：
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. We define causaltopes, our chosen portmanteau of "causal polytopes", for arbitrary spaces of input histories and arbitrary choices of input contexts. We show that causaltopes are obtained by slicing simpler polytopes of conditional probability distributions with a set of causality equations, which we fully characterise. We provide efficient linear programs to compute the maximal component of an empirical model supported by any given sub-causaltope, as well as the associated causal fraction. We introduce a notion of causal separability relative to arbitrary causal constraints. We provide efficient linear programs to compute the maximal causally separable component of an empirical model, and hence its causally separable fraction, as the component jointly supported by certain sub-causaltopes. We study causal fractions and causal separability for several novel examples, including a selection of quantum switches with entangled or contextual control. In the process, we demonstrate the existence of "causal contextuality", a phenomenon where causal inseparability is clearly correlated to, or even directly implied by, non-locality and contextuality.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
