Classical and quantum speed limits

Katarzyna Bolonek-Lasoń1, Joanna Gonera2, and Piotr Kosiński2

1Department of Statistical Methods, Faculty of Economics and Sociology University of Lodz, 41/43 Rewolucji 1905 St., 90-214 Lodz, Poland
2Department of Computer Science, Faculty of Physics and Applied Informatics University of Lodz, 149/153 Pomorska St., 90-236 Lodz, Poland

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Abstract

The new bound on quantum speed limit (in terms of relative purity) is derived by applying the original Mandelstam-Tamm one to the evolution in the space of Hilbert-Schmidt operators acting in the initial space of states. It is shown that it provides the quantum counterpart of the classical speed limit derived in $\textit{Phys. Rev. Lett. 120 (2018), 070402}$ and the $\hbar\rightarrow 0$ limit of the former yields the latter. The existence of classical limit is related to the degree of mixing of the quantum state.

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Cited by

[1] Pablo M. Poggi, Steve Campbell, and Sebastian Deffner, "Diverging Quantum Speed Limits: A Herald of Classicality", PRX Quantum 2 4, 040349 (2021).

[2] Christiane P. Koch, Ugo Boscain, Tommaso Calarco, Gunther Dirr, Stefan Filipp, Steffen J. Glaser, Ronnie Kosloff, Simone Montangero, Thomas Schulte-Herbrüggen, Dominique Sugny, and Frank K. Wilhelm, "Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe", EPJ Quantum Technology 9 1, 19 (2022).

[3] Kang Lan, Shijie Xie, and Xiangji Cai, "Geometric quantum speed limits for Markovian dynamics in open quantum systems", New Journal of Physics 24 5, 055003 (2022).

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