A graph-separation theorem for quantum causal models

Abstract: A causal model is an abstract representation of a physical system as a directed acyclic graph (DAG), where the statistical dependencies are encoded using a graphical criterion called `d-separation'. Recent work by Wood & Spekkens shows that causal models cannot, in general, provide a faithful representation of quantum systems. Since d-separation encodes a form of Reichenbach's Common Cause Principle (RCCP), whose validity is questionable in quantum mechanics, we propose a generalised graph separation rule that does not assume the RCCP. We prove that the new rule faithfully captures the statistical dependencies between observables in a quantum network, encoded as a DAG, and is consistent with d-separation in a classical limit. We note that the resulting model is still unable to give a faithful representation of correlations stronger than quantum mechanics, such as the Popescu-Rorlich box.