Universal Predictors for Mixing Time more than Liouvillian Gap

TL;DR

This paper investigates the factors influencing the mixing time of open quantum systems, revealing that it depends on both the Liouvillian gap and the trace-norm factors of eigenmodes, and provides conditions for rapid mixing.

Contribution

It introduces universal predictors for mixing time based on trace-norm factors and establishes general rapid mixing conditions for various dissipation regimes.

Findings

Mixing time depends on Liouvillian gap and trace-norm factors.

Derived conditions for rapid mixing in strong and weak dissipation regimes.

Framework for designing dissipation to control mixing speed.

Abstract

We analyze the mixing time of open quantum systems governed by the Lindblad master equation, showing that it is determined not only by the Liouvillian gap, but also by the trace-norm factor of each decaying Liouvillian eigenmode. By utilizing them as universal predictors of mixing time, we establish general conditions for the fast and rapid mixing, respectively. Specifically, we derive rapid mixing conditions for both the strong and weak dissipation regimes, formulated as sparsity constraints on the Hamiltonian and the local Lindblad operators. Our findings provide a general framework for calculating mixing time and offer a guide for designing dissipation to achieve desired mixing speeds, which has significant implications for efficient experimental state preparation.