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 and 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 generalized 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 reduces to d -separation in a classical limit.

Keywords

• causality
• bayesian networks
• quantum foundations