Information-Theoretic Implications of Quantum Causal Structures

Abstract: The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional dependencies. In this work, we describe a general algorithm for computing information-theoretic constraints on the correlations that can arise from a given interaction pattern, where we allow for classical as well as quantum variables. We apply the general technique to two relevant cases: First, we show that the principle of information causality appears naturally in our framework and go on to generalize and strengthen it. Second, we derive bounds on the correlations that can occur in a networked architecture, where a set of few-body quantum systems is distributed among a larger number of parties.