Note on the Margolus-Levitin quantum speed limit for arbitrary fidelity

Fuente: arXiv
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Main Authors: Andrzejewski, Krzysztof, Bolonek-Lasoń, Katarzyna, Kosiński, Piotr
Format: Preprint
Published: 2023
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author Andrzejewski, Krzysztof
Bolonek-Lasoń, Katarzyna
Kosiński, Piotr
author_facet Andrzejewski, Krzysztof
Bolonek-Lasoń, Katarzyna
Kosiński, Piotr
contents For vanishing fidelity between initial and final states two important quantum speed limits, the Mandelstam-Tamm limit (involving energy dispersion) and Margolus-Levitin one (involving excitation energy expectation value) have been derived. While the generalization of the former limit to the case of arbitrary fidelity is straightforward, the relevant generalization of the latter, given in the seminal paper by Giovanetti et al (Phys. Rev. A67 (2003), 052109) was based on the conjectured equality of lower and upper bounds on the right hand side of generalized Margolus-Levitin inequality, verified numerically up to seven digits. Only recently there appear two proofs of the conjecture. We provide below a very elementary new proof, based on the simplest tools from differential calculus. Thus the generalized Margolus-Levitin speed limit can be derived much in the spirit of the original one valid for vanishing fidelity.
format Preprint
id arxiv_https___arxiv_org_abs_2307_16854
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Note on the Margolus-Levitin quantum speed limit for arbitrary fidelity
Andrzejewski, Krzysztof
Bolonek-Lasoń, Katarzyna
Kosiński, Piotr
Quantum Physics
For vanishing fidelity between initial and final states two important quantum speed limits, the Mandelstam-Tamm limit (involving energy dispersion) and Margolus-Levitin one (involving excitation energy expectation value) have been derived. While the generalization of the former limit to the case of arbitrary fidelity is straightforward, the relevant generalization of the latter, given in the seminal paper by Giovanetti et al (Phys. Rev. A67 (2003), 052109) was based on the conjectured equality of lower and upper bounds on the right hand side of generalized Margolus-Levitin inequality, verified numerically up to seven digits. Only recently there appear two proofs of the conjecture. We provide below a very elementary new proof, based on the simplest tools from differential calculus. Thus the generalized Margolus-Levitin speed limit can be derived much in the spirit of the original one valid for vanishing fidelity.
title Note on the Margolus-Levitin quantum speed limit for arbitrary fidelity
topic Quantum Physics
url https://arxiv.org/abs/2307.16854