标题： 刻画信号：因果推理与时空几何之间的联系 显示英文标题

标题： Characterizing Signalling: Connections between Causal Inference and Space-time Geometry

摘要： 因果关系对于我们理解世界至关重要，它以不同的形式呈现：信息论的和相对论的，前者与信息流相关，后者与时空结构相关。 利用PRA, 106, 032204 (2022)中引入的一个框架，该框架在一般物理理论中正式连接了这两个概念，我们研究了它们之间的相互作用。 在这里，信息论因果性是通过因果建模的方法来定义的。 首先，我们改进了通过所谓的“影响”关系所定义的信息论信号传递的特征描述。具体来说，我们提供了识别此类关系不同部分冗余性的条件，并引入了在不忠实因果模型（其中可观测数据不能“忠实地”反映因果依赖关系）中的因果推理技术。特别是，这表明可以利用某些节点之间不存在信号传递的可能性来进行因果推理。 其次，我们定义了一个称为“锥性”的序理论性质，显示在具有$d>1$空间维度的闵可夫斯基时空中满足此性质，但在$d=1$中违反此性质。 最后，我们研究了信息论因果模型嵌入时空而不违反相对论原则（如超光速信号禁止NSS）的情况。一般来说，我们观察到时空中的NSS约束与纯粹信息论因果推理的约束表现出不同的行为。 然后我们证明了锥形时空与忠实因果模型之间的对应关系：在这两种情况下，这两种类型的约束都出现了一种平行现象。 这表明信息论和几何学因果概念之间存在联系，并为研究NSS原则和不同时空几何与信息处理理论中的无因果回路原则之间的关系提供了新的见解。 显示英文摘要

摘要： Causality is pivotal to our understanding of the world, presenting itself in different forms: information-theoretic and relativistic, the former linked to the flow of information, the latter to the structure of space-time. Leveraging a framework introduced in PRA, 106, 032204 (2022), which formally connects these two notions in general physical theories, we study their interplay. Here, information-theoretic causality is defined through a causal modelling approach. First, we improve the characterization of information-theoretic signalling as defined through so-called affects relations. Specifically, we provide conditions for identifying redundancies in different parts of such a relation, introducing techniques for causal inference in unfaithful causal models (where the observable data does not "faithfully" reflect the causal dependences). In particular, this demonstrates the possibility of causal inference using the absence of signalling between certain nodes. Second, we define an order-theoretic property called conicality, showing that it is satisfied for light cones in Minkowski space-times with $d>1$ spatial dimensions but violated for $d=1$. Finally, we study the embedding of information-theoretic causal models in space-time without violating relativistic principles such as no superluminal signalling (NSS). In general, we observe that constraints imposed by NSS in a space-time and those imposed by purely information-theoretic causal inference behave differently. We then prove a correspondence between conical space-times and faithful causal models: in both cases, there emerges a parallel between these two types of constraints. This indicates a connection between informational and geometric notions of causality, and offers new insights for studying the relations between the principles of NSS and no causal loops in different space-time geometries and theories of information processing.