Tight, robust, and feasible quantum speed limits for open dynamics

TL;DR

This paper introduces a new, robust quantum speed limit for open quantum systems, applicable to both Markovian and non-Markovian dynamics, which is easier to compute and tighter than previous bounds.

Contribution

It derives a geometric quantum speed limit for open quantum evolution that is robust, easier to compute, and tighter than existing bounds, applicable to various types of open dynamics.

Findings

The new bound is provably robust under composition and mixing.

It is easier to compute and measure than previous bounds.

The bound is tighter than existing bounds for most open processes.

Abstract

Starting from a geometric perspective, we derive a quantum speed limit for arbitrary open quantum evolution, which could be Markovian or non-Markovian, providing a fundamental bound on the time taken for the most general quantum dynamics. Our methods rely on measuring angles and distances between (mixed) states represented as generalized Bloch vectors. We study the properties of our bound and present its form for closed and open evolution, with the latter in both Lindblad form and in terms of a memory kernel. Our speed limit is provably robust under composition and mixing, features that largely improve the effectiveness of quantum speed limits for open evolution of mixed states. We also demonstrate that our bound is easier to compute and measure than other quantum speed limits for open evolution, and that it is tighter than the previous bounds for almost all open processes. Finally, we discuss the usefulness of quantum speed limits and their impact in current research.