Quantum Speed Limit in Terms of Coherence Variations

TL;DR

This paper introduces a quantum speed limit based on coherence variation, showing how quantum states evolve along geodesics under different dynamics, with implications for quantum information processing.

Contribution

It presents a new attainable quantum speed limit related to coherence variation, applicable to 2D quantum states under various dynamical processes.

Findings

Dephasing dynamics can saturate the coherence quantum speed limit.

Decoherence with identical populations occurs faster than with other states.

The proposed bound is tighter compared to previous limits.

Abstract

Coherence is the most fundamental quantum resource in quantum information processing. How fast a physical system gets coherence or decoherence is a critical ingredient. We present an attainable quantum speed limit based on the variation of quantum coherence subject to a dynamical process. It indicates that for a 2-dimensional quantum state, one can always find corresponding dynamics driving it to evolve along the geodesic to another state with certain coherence variation. As applications, we study the coherence quantum speed limits of the dephasing and dissipative dynamics. It is shown that the dephasing dynamics can saturate our coherence quantum speed limit, and the decoherence of the state with identical populations will be faster than others. However, the dissipative dynamics have the opposite behavior. In addition, we illustrate a stronger tightness of our bound for the mentioned dynamics by comparison.