Quantum speed limit for states and observables of perturbed open systems

TL;DR

This paper introduces a new quantum speed limit for open systems under perturbations, linking the divergence rate to quantum Fisher information and enabling practical applications in estimating system properties and understanding non-equilibrium dynamics.

Contribution

It establishes a novel speed limit for perturbed open quantum systems, connecting divergence speed to quantum Fisher information and providing practical bounds for observable responses.

Findings

Divergence speed bounded by quantum Fisher information.

Allows experimental estimation of Fisher information with decoherence.

Shows large work fluctuations are needed for rapid non-equilibrium transitions.

Abstract

Quantum speed limits provide upper bounds on the rate with which a quantum system can move away from its initial state. Here, we provide a different kind of speed limit, describing the divergence of a perturbed open system from its unperturbed trajectory. In the case of weak coupling, we show that the divergence speed is bounded by the quantum Fisher information under a perturbing Hamiltonian, up to an error which can be estimated from system and bath timescales. We give two applications of our speed limit. Firstly, it enables experimental estimation of quantum Fisher information in the presence of decoherence that is not fully characterised. Secondly, it implies that large quantum work fluctuations are necessary for a thermal system to be driven quickly out of equilibrium under a quench. Moreover, it can be used to bound the response to perturbations of expectation values of observables in open systems.