Speed limits of the trace distance for open quantum system

Abstract

We investigate the speed limit of the state transformation in open quantum systems described by the Lindblad type quantum master equation. We obtain universal bounds of the total entropy production described by the trace distance between the initial and final states in the interaction picture. Beyond a previous study by Vu and Saito [Phys. Rev. Lett. 128, 010602 (2022)] applicable only to the completely mixed initial state, our results are applicable to an arbitrary initial state. Our bounds can be tighter than the bound of Vu and Hasegawa [Phys. Rev. Lett. 126, 010601 (2021)] which measures the distance by the modified Wasserstein distance dT : For a system of which Hilbert space is two-dimensional, the trace distance is greater than or equal to dT . For this reason, our results can significantly improve Vu-Hasegawa's bound.