Classical and quantum speed limits

Quantum 5, 482 (2021).

https://doi.org/10.22331/q-2021-06-24-482

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 $hbarrightarrow 0$ limit of the former yields the latter. The existence of classical limit is related to the degree of mixing of the quantum state.