# Analysing causal structures in generalised probabilistic theories

## TL;DR

This paper develops a method using measurement entropy to analyze and differentiate causal structures across classical, quantum, and generalized probabilistic theories, providing new insights and minimal constraints for causal explanations.

## Contribution

It introduces a measurement entropy-based approach for comparing causal structures in various theories, including quantum and classical, and proves the convexity of achievable entropy vectors.

## Key findings

- Derived new relations separating classical, quantum, and general theories.
- Established minimal constraints for causal explanations in generalized theories.
- Proved the convexity of entropy vector sets in any causal structure.

## Abstract

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad range of theories, which include both quantum and classical theory as special cases. We propose a method for analysing differences between such theories based on the so-called measurement entropy. We apply this method to several causal structures, deriving new relations that separate classical, quantum and more general theories within these causal structures. The constraints we derive for the most general theories are in a sense minimal requirements of any causal explanation in these scenarios. In addition, we make several technical contributions that give insight for the entropic analysis of quantum causal structures. In particular, we prove that for any causal structure and for any generalised probabilistic theory, the set of achievable entropy vectors form a convex cone.