Rapid mixing and stability of quantum dissipative systems

TL;DR

This paper demonstrates that in quantum many-body systems with local interactions, rapid mixing ensures the stability of local observables and correlation functions against local perturbations, highlighting robustness in modeling and quantum information processing.

Contribution

It proves that rapid mixing and a unique fixed point guarantee stability of local observables in quantum dissipative systems without additional conditions.

Findings

Local observables are stable under local perturbations.

Correlation functions remain robust if the system is rapidly mixing.

Stability holds with only rapid mixing and a unique fixed point.

Abstract

The physics of many materials is modeled by quantum many-body systems with local interactions. If the model of the system is sensitive to noise from the environment, or small perturbations to the original interactions, it will not properly model the robustness of the real physical system it aims to describe, or be useful when engineering novel systems for quantum information processing. We show that local observables and correlation functions of local Liouvillians are stable to local perturbations if the dynamics is rapidly mixing and has a unique fixed point. No other condition is required.