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Margolus-Levitin quantum speed limit for an arbitrary fidelity
University of Luxembourg, Luxembourg.ORCID iD: 0000-0002-2005-8694
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1726-4892
2023 (English)In: Physical Review Research, E-ISSN 2643-1564, Vol. 5, no 4, article id 043234Article in journal (Refereed) Published
Abstract [en]

The Mandelstam-Tamm and Margolus-Levitin quantum speed limits are two well-known evolution time estimates for isolated quantum systems. These bounds are usually formulated for fully distinguishable initial and final states, but both have tight extensions to systems that evolve between states with an arbitrary fidelity. However, the foundations of these extensions differ in some essential respects. The extended Mandelstam-Tamm quantum speed limit has been proven analytically and has a clear geometric interpretation. Furthermore, which systems saturate the limit is known. The derivation of the extended Margolus-Levitin quantum speed limit, on the other hand, is based on numerical estimates. Moreover, the limit lacks a geometric interpretation, and no complete characterization of the systems reaching it exists. In this paper, we derive the extended Margolus-Levitin quantum speed limit analytically and describe the systems that saturate the limit in detail. We also provide the limit with a symplectic-geometric interpretation, which indicates that it is of a different character than most existing quantum speed limits. At the end of the paper, we analyze the maximum of the extended Mandelstam-Tamm and Margolus-Levitin quantum speed limits and derive a dual version of the extended Margolus-Levitin quantum speed limit. The maximum limit is tight regardless of the fidelity of the initial and final states. However, the conditions under which the maximum limit is saturated differ depending on whether or not the initial state and the final state are fully distinguishable. The dual limit is also tight and follows from a time reversal argument. We describe the systems that saturate the dual quantum speed limit. 

Place, publisher, year, edition, pages
American Physical Society, 2023. Vol. 5, no 4, article id 043234
Keywords [en]
Closed systems, Evolution time, Expected energy, Isolated systems, Speed limit, Quantum theory
National Category
Physical Sciences
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-97813DOI: 10.1103/physrevresearch.5.043234ISI: 001128791000001Scopus ID: 2-s2.0-85179628087OAI: oai:DiVA.org:kau-97813DiVA, id: diva2:1821211
Available from: 2023-12-19 Created: 2023-12-19 Last updated: 2024-01-16Bibliographically approved

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Sönnerborn, Ole

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