Quantum speed limits in open systems: non-Markovian dynamics without rotating-wave approximation.

Zhe Sun,Jian Ma,Jing Liu,Xiaoguang Wang

doi:10.1038/srep08444

Abstract

We derive an easily computable quantum speed limit (QSL) time bound for open systems whose initial states can be chosen as either pure or mixed states. Moreover, this QSL time is applicable to either Markovian or non-Markovian dynamics. By using of a hierarchy equation method, we numerically study the QSL time bound in a qubit system interacting with a single broadened cavity mode without rotating-wave, Born and Markovian approximation. By comparing with rotating-wave approximation (RWA) results, we show that the counter-rotating terms are helpful to increase evolution speed. The problem of non-Markovianity is also considered. We find that for non-RWA cases, increasing system-bath coupling can not always enhance the non-Markovianity, which is qualitatively different from the results with RWA. When considering the relation between QSL and non-Markovianity, we find that for small broadening widths of the cavity mode, non-Markovianity can increase the evolution speed in either RWA or non-RWA cases, while, for larger broadening widths, it is not true for non-RWA cases.

Highlights

We derive an computable quantum speed limit (QSL) time bound for open systems whose initial states can be chosen as either pure or mixed states
As a fundamental law of nature, provides ultimate constraints known as quantum speed limits (QSLs) which are virtually at the center of all areas of quantum physics and they are of manifold applications, including exploring the physical limits of computation[1], providing fundamental limit of precision under quantum metrology[2,3], restricting efficiency of quantum optimal control algorithms[4,5] and providing a minimal time bound to perform the optimal process[6]
We have derived a computable QSL time bound which can be applied in the open systems of mixed initial states undergoing nonMarkovian dynamics

Summary

Introduction

We derive an computable quantum speed limit (QSL) time bound for open systems whose initial states can be chosen as either pure or mixed states This QSL time is applicable to either Markovian or non-Markovian dynamics. Del Campo et al.[17] employed the concept of relative purity to derive an analytical and computable QSL time for open systems undergoing a completely positive and trace preserving evolution Their bound accounts for the non-Markovian dynamics. Deffner and Lutz[18] formulated a tight bound on the minimal evolution time of an arbitrarily driven open system, and showed that non-Markovian effects can speed up quantum evolution Their time bound is derived from pure initial states and can not be directly applied into the mixed initial states

Methods

Results

Conclusion