The entropic approach to causal correlations

Abstract

The existence of a global causal order between events places constraints on\nthe correlations that parties may share. Such "causal correlations" have been\nthe focus of recent attention, driven by the realization that some extensions\nof quantum mechanics may violate so-called causal inequalities. In this paper\nwe study causal correlations from an entropic perspective, and we show how to\nuse this framework to derive entropic causal inequalities. We consider two\ndifferent ways to derive such inequalities. Firstly, we consider a method based\non the causal Bayesian networks describing the causal relations between the\nparties. In contrast to the Bell-nonlocality scenario, where this method has\npreviously been shown to be ineffective, we show that it leads to several\ninteresting entropic causal inequalities. Secondly, we consider an alternative\nmethod based on counterfactual variables that has previously been used to\nderive entropic Bell inequalities. We compare the inequalities obtained via\nthese two methods and discuss their violation by noncausal correlations. As an\napplication of our approach, we derive bounds on the quantity of information -\nwhich is more naturally expressed in the entropic framework - that parties can\ncommunicate when operating in a definite causal order.\n