Quantum speed limit time: role of coherence

TL;DR

This paper investigates how initial coherence and mixedness influence the quantum speed limit time in multi-qubit states under non-Markovian channels, revealing their roles in quantum evolution and potential as dynamical witnesses.

Contribution

It introduces a detailed analysis of the impact of initial coherence and mixedness on quantum speed limits for multi-qubit states in non-Markovian environments, highlighting differences between unital and non-unital channels.

Findings

Initial coherence affects speed limit time under information backflow.

Trade-off between mixedness and coherence influences quantum evolution.

Speed limit time can distinguish between unital and non-unital channels.

Abstract

The minimum evolution time between multi-qubit quantum states is estimated for non-Markovian quantum channels. We consider the maximally coherent pure and mixed states as well as multi-qubit $X$ states as initial states and discuss the impact of initial coherence and the behaviour of coherence on their speed of evolution for both dephasing and dissipative processes. The role of the non-zero value of initial coherence under information backflow conditions for the non-unital dissipative process is revealed by the flow of quantum speed limit time ($\tau_{QSL}$). The trade-off between mixedness and coherence on the speed limit time reveals the nature of the quantum process the states undergo. The complementarity effect between mixedness and coherence is more prominent in the quantum non-unital dissipation process. The parametric trajectory of speed limit time vividly depicts the difference in the evolution of pure and mixed initial states, and this could be used to distinguish between the unital and non-unital channels studied in this work. Our investigation of quantum speed limit time on multi-qubit entangled $X$ states reveals that $\tau_{QSL}$ can be identified as a potential dynamical witness to distinguish multi-qubit states in the course of evolution.