  A state on a tripartite quantum system $A \otimes B \otimes C$ forms a Markov
chain if it can be reconstructed from its marginal on $A \otimes B$ by a
quantum operation from $B$ to $B \otimes C$. 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.
