Speed limits of the trace distance for open quantum system

TL;DR

This paper establishes tighter universal bounds on the speed of state transformations in open quantum systems using trace distance, improving previous bounds and applicable to systems described by Lindblad equations.

Contribution

It derives universal bounds on entropy production in open quantum systems that are tighter than previous bounds, enhancing understanding of quantum speed limits.

Findings

Bounds are tighter than Vu and Hasegawa's previous bounds.

Trace distance in Schrödinger picture bounded by interaction picture and unitary dynamics.

Results applicable to Lindblad-type quantum master equations.

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. Our bounds can be tighter than the bound of Vu and Hasegawa [Phys. Rev. Lett. 126, 010601 (2021)] which measures the distance by the eigenvalues of the initial and final states: This distance is less than or equal to the trace distance. For this reason, our results can significantly improve Vu-Hasegawa's bound. The trace distance in the Schr\"{o}dinger picture is bounded by a sum of the trace distance in the interaction picture and the trace distance for unitary dynamics described by only the Hamiltonian in the quantum master equation.