Indistinguishability of causal relations from limited marginals

TL;DR

This paper explores whether different causal relations can be distinguished using limited marginal data, introducing adhesivity as a key tool to identify indistinguishable causal structures and simplify their characterization.

Contribution

It introduces the concept of adhesivity to analyze causal indistinguishability from limited marginals and provides criteria for recognizing when causal structures cannot be distinguished.

Findings

Provides a criterion for indistinguishability of causal structures with limited marginals

Simplifies characterization of marginal scenarios using adhesivity

Facilitates derivation of Bell inequalities and identification of classical, quantum, and postquantum probabilities

Abstract

We investigate the possibility of distinguishing among different causal relations starting from a limited set of marginals. Our main tool is the notion of adhesivity, that is, the extension of probability or entropies defined only on subsets of variables, which provides additional independence constraints among them. Our results provide a criterion for recognizing which causal structures are indistinguishable when only limited marginal information is accessible. Furthermore, the existence of such extensions greatly simplifies the characterization of a marginal scenario, a result that facilitates the derivation of Bell inequalities both in the probabilistic and entropic frameworks, and the identification of marginal scenarios where classical, quantum, and postquantum probabilities coincide.