Quantum Conditional Mutual Information and Approximate Markov Chains 论文

摘要

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.