Generalized Geometric Quantum Speed Limits

TL;DR

This paper introduces a family of generalized quantum speed limits using information geometry, improving bounds on quantum evolution times and impacting quantum technology optimization and fundamental physics.

Contribution

It establishes an infinite family of quantum speed limits based on information geometry, unifying and extending previous bounds with tighter, more versatile constraints.

Findings

Derived new bounds that outperform traditional quantum Fisher information limits.

Showed the importance of different information metrics in open system dynamics.

Clarified roles of classical populations and quantum coherences in speed limits.

Abstract

The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the non uniqueness of a bona fide measure of distinguishability defined on the quantum state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits, and provides instances of novel bounds which are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.