Modified quantum-speed-limit bounds for open quantum dynamics in quantum channels

TL;DR

This paper investigates the apparent violations of quantum-speed-limit bounds in open quantum systems, revealing they are due to numerical precision limits and proposing a method to correct these estimates.

Contribution

It introduces a generic approach to overcome inconsistent quantum-speed-limit estimates caused by finite numerical precision in open quantum dynamics.

Findings

Inconsistencies occur when numerical resolution limits are reached.

The proposed method effectively corrects QSL estimates in amplitude- and phase-damping channels.

Special cases may restrict the QSL bound based on quantum properties.

Abstract

The minimal evolution time between two distinguishable states is of fundamental interest in quantum physics. Very recently Mirkin et al. argue that some most common quantum-speed-limit (QSL) bounds which depend on the actual evolution time do not cleave to the essence of the QSL theory as they grow indefinitely but the final state is reached at a finite time in a damped Jaynes-Cummings (JC) model. In this paper, we thoroughly study this puzzling phenomenon. We find the inconsistent estimates will happen if and only if the limit of resolution of a calculation program is achieved, through which we propose that the nature of the inconsistency is not a violation to the essence of the QSL theory but an illusion caused by the finite precision in numerical simulations. We also present a generic method to overcome the inconsistent estimates and confirm its effectiveness in both amplitude-damping and phase-damping channels. Additionally, we show special cases which may restrict the QSL bound defined by "quantumness".