Comment on "Energy-time uncertainty relation for driven quantum systems" and "Quantum Speed Limit for Non-Markovian Dynamics"

TL;DR

This paper critiques previous extensions of quantum speed limits to non-Markovian and time-dependent systems, clarifying the correct applicability of the Mandelstam-Tamm and Margolus-Levitin bounds.

Contribution

It corrects the analysis of the Margolus-Levitin bound in non-Markovian, time-dependent quantum systems and clarifies its valid scope.

Findings

Mandelstam-Tamm bound derivation is correct.

Margolus-Levitin bound analysis is incorrect for non-adiabatic systems.

Margolus-Levitin bound is only established for adiabatic time-dependent systems.

Abstract

Deffner and Lutz [J. Phys. A 46, 335302 (2013) and Phys. Rev. Lett. 111, 010402 (2013).] extended the Mandelstam-Tamm bound and the Margolus-Levitin bound to time-dependent and non-Markovian systems, respectively. Although the derivation of the Mandelstam-Tamm bound is correct, we point out that thier analysis of the Margolus-Levitin bound is incorrect. The Margolus-Levitin bound has not yet been established in time-dependent quantum systems, except for the adiabatic case.