Quantitative propagation of chaos for Lindblad dynamics

TL;DR

This paper proves that in open quantum systems described by Lindblad equations, the many-body dynamics converges to a mean-field limit with explicit bounds, demonstrating quantitative propagation of chaos.

Contribution

It provides the first explicit $1/N$ bounds on the quantum relative entropy between $N$-particle states and their mean-field limits.

Findings

Convergence of $N$-body Lindblad dynamics to mean-field equations.

Explicit $1/N$ bounds on quantum relative entropy.

Quantitative propagation of chaos in open quantum systems.

Abstract

We consider an open quantum system governed $N$-body Lindblad equation and study mean-field limits in this setting. We prove that the $N$-particle dynamics converges, in the sense of quantum relative entropy, to the tensorized solution of the limiting nonlinear equation. More precisely, we establish explicit bounds of order $1/N$ on the relative entropy between the $N$-particle density operator and the corresponding product state, thereby providing a quantitative propagation of chaos.