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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