Inferring Causal Structure from Statistical Dependences among n Variables — Differences between Classical and Quantum Communication Scenarios

Dr. Dominik Janzing
Germany, Max Planck Institute for Intelligent Systems
Statistical dependences between n observed random variables reveal some information about the underlying causal structure: if the causal structure is described by a directed acyclic graph (DAG) whose arrows describe direct influence, the causal Markov condition states that every variable is conditionally independent of its non-descendants, given its parents.
More recently it has been recognized that causal inference based on conditional independences alone is insufficient for several reasons:
First, there are asymmetries between cause and effect that cannot be phrased in terms of conditional statistical independences.
Second, causal structures that involve latent common causes imply information-theoretic constraints beyond independences. Remarkably, these constraints are the generalized Bell-inequalities recently considered in the context of the foundations of quantum theory. These inequalities describe the set of multipartite joint distributions that can be generated by a certain classical communication scenario (i.e., by a certain causal structure). If the parties exchange quantum information, the same causal DAG may generate stronger dependences. In this sense, quantum communication is more efficient.
The talk will describe some recent proposals for causal inference in the classical world that use properties of joint distributions other than statistical independences.
Moreover, I will sketch why substantially different causal inference rules are valid when causes influence their effects by sending quantum systems as information carriers.
These insights may be crucial for a future understanding of the power and limits of quantum computing.