Quantum Speed Limits Across the Quantum-to-Classical Transition

TL;DR

This paper explores quantum speed limits and their classical counterparts using a phase-space approach, revealing that speed limits exist across the quantum-to-classical transition and are governed by the generator of evolution.

Contribution

It introduces a unified phase-space framework to identify and compare speed limits in quantum and classical systems, challenging the belief that such limits are exclusive to quantum mechanics.

Findings

Speed limits exist in both quantum and classical systems.

Classical speed limits are determined by the norm of the generator of evolution.

Quantum and classical bounds are equivalent in the phase-space formulation.

Abstract

Quantum speed limits set an upper bound to the rate at which a quantum system can evolve. Adopting a phase-space approach we explore quantum speed limits across the quantum to classical transition and identify equivalent bounds in the classical world. As a result, and contrary to common belief, we show that speed limits exist for both quantum and classical systems. As in the quantum domain, classical speed limits are set by a given norm of the generator of time evolution.