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The classical version of Mandelstam-Tamm speed limit based on the Wignerfunction in phase space is reported by B. Shanahan et al. [Phys. Rev. Lett.120, 070401 (2018)]. In this paper, the Margolus-Levitin speed limit across thequantum-to-classical transition is given in phase space based on the tracedistance. The Margolus-Levitin speed limit is set by the Schatten L1 norm ofthe generator of time dependent evolution for both the quantum and classicaldomains. As an example, the time-dependent harmonic oscillator is considered toillustrate the result.

Margolus-Levitin speed limit across quantum to classical regimes based on trace distance