Quantum Speed Limit is Not Quantum

TL;DR

This paper demonstrates that the quantum speed limit (QSL) is not exclusive to quantum mechanics but also applies to classical systems, revealing it as a universal property of Hilbert space.

Contribution

The authors derive a classical speed limit analogous to the QSL, showing its universality across classical and quantum dynamics within the Hilbert space framework.

Findings

Classical mechanics has a fundamental speed limit similar to QSL.

QSL is a universal dynamical property, not unique to quantum systems.

Speed limits are also applicable to imaginary-time Schrödinger equations like the master equation.

Abstract

The quantum speed limit (QSL), or the energy-time uncertainty relation, describes the fundamental maximum rate for quantum time evolution and has been regarded as being unique in quantum mechanics. In this study, we obtain a classical speed limit corresponding to the QSL using the Hilbert space for the classical Liouville equation. Thus, classical mechanics has a fundamental speed limit, and QSL is not a purely quantum phenomenon but a universal dynamical property of the Hilbert space. Furthermore, we obtain similar speed limits for the imaginary-time Schroedinger equations such as the master equation.