Conditional mutual information and self-commutator

TL;DR

This paper introduces a simplified method to characterize when conditional mutual information vanishes, linking it to commutators, and explores its implications for quantum Markov chains and approximate SSA.

Contribution

It proposes a new approach connecting conditional mutual information to commutators, advancing understanding of quantum Markov chains and approximate strong subadditivity.

Findings

Relates vanishing conditional mutual information to commutators.

Suggests small conditional mutual information implies small perturbation of quantum Markov chains.

Provides remarks on the implications for approximate SSA.

Abstract

A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach towards the approximate version of SSA. That is, it is conjectured that small conditional mutual information implies small perturbation of quantum Markov chain.