Stability of local quantum dissipative systems

TL;DR

This paper demonstrates that local observables and correlations in quantum dissipative systems remain stable under certain perturbations, provided the system has a unique fixed point and rapid mixing, using Lieb-Robinson bounds.

Contribution

It establishes stability of local quantum dissipative systems under polynomially decaying perturbations, extending understanding of robustness in open quantum many-body dynamics.

Findings

Stability of local observables under perturbations with logarithmic mixing time

Applicability to classical Glauber dynamics with non-detailed balance perturbations

Use of Lieb-Robinson bounds to prove finite information propagation speed

Abstract

Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These local perturbations are potentially unbounded, but constrained to respect the underlying lattice structure. We show that even for polynomially decaying errors in the Lindbladian, local observables and correlation functions are stable if the unperturbed Lindbladian has a unique fixed point and a mixing time which scales logarithmically with the system size. The proof relies on Lieb-Robinson bounds, which describe a finite group velocity for propagation of information in local systems. As a main example, we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates which may not preserve detailed balance.