Energy-time uncertainty relation for driven quantum systems

TL;DR

This paper generalizes the energy-time uncertainty relation for driven quantum systems using a geometric approach, providing explicit formulas for quantum speed limits applicable to any states and protocols, thus defining fundamental evolution rate limits.

Contribution

It introduces a geometric method to derive quantum speed limits for driven systems, extending the energy-time uncertainty relation to arbitrary states and protocols.

Findings

Derived explicit quantum speed limit formulas

Established fundamental limits on quantum evolution rates

Applicable to arbitrary initial/final states and driving protocols

Abstract

We derive generalizations of the energy-time uncertainty relation for driven quantum systems. Using a geometric approach based on the Bures length between mixed quantum states, we obtain explicit expressions for the quantum speed limit time, valid for arbitrary initial and final quantum states and arbitrary driving protocols. Our results establish the fundamental limit on the rate of evolution of generic quantum systems.