Margolus–Levitin speed limit across quantum to classical regimes based on trace distance**Project supported by the National Natural Science Foundation of China (Grant No. 11775040), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province of China (Grant No. 2019L0527), and the Fundamental Research Fund for the Central Universities of China (Grant No. DUT18LK45).

Abstract

The classical version of Mandelstam–Tamm speed limit based on the Wigner function in phase space was reported by Shanahan et al. [Phys. Rev. Lett. 120 070401 (2018)]. We present the Margolus–Levitin speed limit across the quantum-to-classical transition in phase space based on the trace distance. The Margolus–Levitin speed limit is set by the Schatten L1 norm of the generator of time-dependent evolution for both the quantum and classical domains. As an example, the time-dependent harmonic oscillator is considered to illustrate the result.