Quantum Conditional Mutual Information and Approximate Markov Chains

Abstract

A state on a tripartite quantum system A⊗B⊗C forms a Markov chain if it can be reconstructed from its marginal on A⊗B by a quantum operation from B to B⊗C. We show that the quantum conditional mutual information I(A : C|B) of an arbitrary state is an upper bound on its distance to the closest reconstructed state. It thus quantifies how well the Markov chain property is approximated.