Quantum conditional mutual information and approximate Markov chains

TL;DR

This paper establishes that quantum conditional mutual information quantifies how closely a tripartite quantum state approximates a Markov chain, providing a measure of the Markov property’s approximation in quantum systems.

Contribution

It proves that quantum conditional mutual information bounds the distance to the nearest Markov chain state, linking information measures to state reconstruction.

Findings

Quantum conditional mutual information bounds the approximation quality of Markov chains.

The work provides a quantitative measure for how well a quantum state approximates a Markov chain.

Establishes a fundamental relation between information theory and quantum state reconstruction.

Abstract

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.