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.

翻译：我们为因果性、非定域性与情境性的研究提供了一个统一的、完全设备无关且理论无关的操作性框架。我们定义"因果多面体"（causaltopes）——即"Causal Polytopes"的自创合成词——适用于任意输入历史空间和任意输入情境选择。研究表明，因果多面体可通过一组我们完全刻画其性质的因果方程，对更简单的条件概率分布多面体进行切割获得。我们提供了有效的线性规划方法，用以计算经验模型在任意给定子因果多面体上的最大支撑成分及其关联因果份额。针对任意因果约束，我们引入了因果可分性的概念；并给出线性规划，通过计算经验模型由特定子因果多面体联合支撑的最大因果可分成分及其因果可分份额。通过若干新案例（包括纠缠或情境控制的量子开关选择），我们研究了因果份额与因果可分性。在此过程中，我们证实了"因果情境性"现象——其中因果不可分性与非定域性及情境性存在明显相关，甚至直接由其推导得出。