Quantum Speed Limit under Brachistochrone Evolution

TL;DR

This paper introduces a geometrical method to derive a quantum speed limit bound applicable to both closed and open quantum systems, emphasizing the role of individual parameter dynamics in quantum evolution.

Contribution

It presents a novel geometrical approach using Riemannian metrics to establish a quantum speed limit bound for general quantum problems, including open systems.

Findings

The new bound accounts for the dynamics of critical parameters.

The approach provides tighter QSL bounds in example scenarios.

It advances understanding of quantum evolution time constraints.

Abstract

According to the Heisenberg uncertainty principle between time and energy fluctuation, a concept of the quantum speed limit (QSL) has been established to determine the minimum evolutionary time between quantum states. Considerable theoretical and experimental efforts are invested in obtaining the QSL time bounds in various scenarios. However, it remains a long-standing goal to derive a meaningful QSL bound for a general quantum problem. Here, we propose a geometrical approach to derive a QSL bound for closed and open quantum systems. By solving a quantum brachistochrone problem in the framework of the Riemannian metric, we show that the QSL between a given initial state to a final state is determined not only by the entire dynamics of the system but also by the individual dynamics of a critical parameter. We exemplify the utility of the new bound in three representative scenarios, demonstrating a pronounced advantage in finding a tight and meaningful QSL bound of a general quantum evolution problem.