• Open Access

Operational definition of a quantum speed limit

Yanyan Shao, Bo Liu, Mao Zhang, Haidong Yuan, and Jing Liu
Phys. Rev. Research 2, 023299 – Published 8 June 2020

Abstract

The quantum speed limit is a fundamental concept in quantum mechanics, which aims at finding the minimum time scale or the maximum dynamical speed for some fixed targets. In a large number of studies in this field, the construction of valid bounds for the evolution time is always the core mission, yet the physics behind it and some fundamental questions like which states can really fulfill the target are ignored. Understanding the physics behind the bounds is at least as important as constructing attainable bounds. Here we provide an operational approach for the definition of the quantum speed limit, which utilizes the set of states that can fulfill the target to define the speed limit. Its performances in various scenarios have been investigated. For time-independent Hamiltonians, it is inverse proportional to the difference between the highest and lowest energies. The fact that its attainability does not require a zero ground-state energy suggests it can be used as an indicator of quantum phase transitions. For time-dependent Hamiltonians, it is shown that, contrary to the results given by existing bounds, the true speed limit should be independent of the time. Moreover, in the case of spontaneous emission, we find a counterintuitive phenomenon that a lousy purity can benefit the reduction of the quantum speed limit.

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  • Received 2 October 2019
  • Revised 25 February 2020
  • Accepted 19 May 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.023299

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Yanyan Shao1, Bo Liu2, Mao Zhang1, Haidong Yuan3, and Jing Liu1,*

  • 1MOE Key Laboratory of Fundamental Physical Quantities Measurement and Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
  • 2Beijing Computational Science Research Center, Beijing 100193, China
  • 3Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong

  • *liujingphys@hust.edu.cn

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Vol. 2, Iss. 2 — June - August 2020

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