The initial-state dependence of quantum speed limit

TL;DR

This paper investigates how the initial state of a qubit influences the quantum speed limit, revealing that initial-state dependence is crucial and can lead to different predictions about quantum evolution speedup.

Contribution

It introduces a new bound for quantum speed limit time that emphasizes the importance of initial-state dependence over non-Markovianity or excited state population.

Findings

Initial-state dependence significantly affects quantum speed limits.

Non-Markovianity and excited state population may not indicate evolution acceleration.

Different quantum speed limits can give contradictory predictions.

Abstract

The generic bound of quantum speed limit time (the minimal evolution time) for a qubit system interacting with structural environment is investigated. We define a new bound for the quantum speed limit. It is shown that the non-Markovianity and the population of the excited state can fail to signal the quantum evolution acceleration, but the initial-state dependence is an important factor. In particular, we find that different quantum speed limits could produce contradictory predictions on the quantum evolution acceleration.