Quantum speed limits on operator flows and correlation functions

TL;DR

This paper generalizes quantum speed limits to operator flows, providing bounds on the evolution of quantum systems and their correlation functions, with implications for quantum dynamics and parameter estimation.

Contribution

It introduces a novel generalization of quantum speed limits for unitary operator flows and applies these to correlation functions and quantum Fisher information.

Findings

Derived two types of quantum speed limits for operator flows

Illustrated the bounds with a qubit and random matrix Hamiltonian

Provided constraints on quantum dynamical response and parameter estimation

Abstract

Quantum speed limits (QSLs) identify fundamental time scales of physical processes by providing lower bounds on the rate of change of a quantum state or the expectation value of an observable. We introduce a generalization of QSL for unitary operator flows, which are ubiquitous in physics and relevant for applications in both the quantum and classical domains. We derive two types of QSLs and assess the existence of a crossover between them, that we illustrate with a qubit and a random matrix Hamiltonian, as canonical examples. We further apply our results to the time evolution of autocorrelation functions, obtaining computable constraints on the linear dynamical response of quantum systems out of equilibrium and the quantum Fisher information governing the precision in quantum parameter estimation.