Quantitative propagation of chaos for Lindblad dynamics

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.