Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter

TL;DR

This paper proves that in gapped quantum phases, mutual information and conditional mutual information decay superpolynomially, establishing a universal property across various systems and phases, including chiral phases.

Contribution

It demonstrates the universal superpolynomial decay of mutual information in gapped quantum phases, extending the understanding to pure and mixed states and refining phase classifications.

Findings

Superpolynomial decay of mutual information in gapped phases

Universal property across pure and mixed states

Decay also holds in chiral phases

Abstract

For spin and fermionic systems in any spatial dimension, we establish that the superpolynomial decay behavior of mutual information and conditional mutual information is a universal property of gapped pure- and mixed-state phases; i.e., all systems in such a phase possess this property if one system in this phase possesses this property. We further demonstrate that the (conditional) mutual information indeed decays superpolynomially in a large class of phases, including chiral phases. As a by-product, we sharpen the notion of mixed-state phases.