Indistinguishability of causal relations from limited marginals

Understand

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.