Information-Theoretic Implications of Classical and Quantum Causal Structures

Inferring causal relationships from empirical data is one of the main goals of science. To that aim a simple but crucial observation is that the correlations that can be observed between a set of variables depend on the causal structure underpinning them. Within that context, during the past year we have developed and formalized a new research program for the study of causal relations between classical as well as quantum variables. What we propose is an information-theoretic framework for computing constraints that a causal structure can give rise to. We illustrate the power and generality of our method by applying it to a variety of classical and quantum scenarios: i) inferring the direction of causation from marginal observations, ii) the quantification of direct causal influence in classical models, iii) the derivation of constraints implied by the topology of distributed quantum architectures and iv) a strengthened version of the information causality principle. The root of this research program lies in previous work on Bell’s theorem [1–4], that we have adapted and generalized for its use in classical causal inference problems [5] and that in our most recent work [6] has been tailored to deal with quantum causal inference problems as well. The undergoing evolution of this program highlights a fruitful interplay between the causal inference literature and problems in quantum information, in particular nonlocality, a connection which is increasingly appreciated among quantum physicists.