Mixing Time of Open Quantum Systems via Hypocoercivity

TL;DR

This paper introduces a new theoretical framework for estimating the mixing time of open quantum systems by separating Hamiltonian and dissipative components, inspired by hypocoercivity, avoiding spectral gap estimation.

Contribution

It presents a novel hypocoercivity-based approach to analyze mixing times in open quantum systems, applicable to systems difficult to analyze with traditional spectral gap methods.

Findings

Provides mixing time estimates for specific quantum systems

Circumvents the need for spectral gap estimation

Applicable to classes of systems with complex dynamics

Abstract

Understanding the mixing of open quantum systems is a fundamental problem in physics and quantum information science. Existing approaches for estimating the mixing time often rely on the spectral gap estimation of the Lindbladian generator, which can be challenging to obtain in practice. We propose a novel theoretical framework to estimate the mixing time of open quantum systems that treats the Hamiltonian and dissipative part separately, thus circumventing the need for a priori estimation of the spectral gap of the full Lindbladian generator. This framework yields mixing time estimates for a class of quantum systems that are otherwise hard to analyze, even though it does not apply to arbitrary Lindbladians. The technique is based on the construction of an energy functional inspired by the hypocoercivity of (classical) kinetic theory.