Quantum Speed Limit Bounds in an Open Quantum Evolution

TL;DR

This paper systematically analyzes quantum speed limit bounds in the damped Jaynes-Cummings model, revealing that only one bound aligns with foundational QSL theory and that non-Markovian effects generally accelerate quantum evolution.

Contribution

It provides a comprehensive comparison of QSL bounds in a specific open quantum system, highlighting their limitations and the influence of non-Markovian effects.

Findings

Only one QSL bound aligns with original QSL theory.

Non-Markovian effects tend to speed up quantum evolution.

QSL bounds alone cannot determine Markovian or non-Markovian behavior.

Abstract

Quantum mechanics dictates bounds for the minimal evolution time between predetermined initial and final states. Several of these Quantum Speed Limit (QSL) bounds were derived for non-unitary dynamics using different approaches. Here, we perform a systematic analysis of the most common QSL bounds in the damped Jaynes-Cummings model, covering the Markovian and non-Markovian regime. We show that only one of the analysed bounds cleaves to the essence of the QSL theory outlined in the pioneer works of Mandelstam \& Tamm and Margolus \& Levitin in the context of unitary evolutions. We also show that all of QSL bounds analysed reflect the fact that in our model non-Markovian effects speed up the quantum evolution. However, it is not possible to infer the Markovian or non-Markovian behaviour of the dynamics only analysing the QSL bounds.