Quantum Speed Limits under Continuous Quantum Measurements

TL;DR

This paper investigates how continuous quantum measurements affect the speed limits of quantum system evolution, revealing violations of standard bounds and characterizing the stochastic dynamics induced in Hilbert space.

Contribution

It introduces a detailed analysis of quantum speed limits under continuous measurements, showing trajectory-dependent violations and Brownian motion effects in Hilbert space.

Findings

Standard quantum speed limits can be violated in certain measurement trajectories.

Continuous measurements induce Brownian dynamics in the quantum state space.

The dispersion and full statistics of evolution speeds are characterized.

Abstract

The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. We consider the speed of evolution for quantum systems undergoing stochastic dynamics due to continuous measurements. It is shown that that there are trajectories for which standard QSL are violated, and we provide estimates for the range of velocities in an ensemble of realizations of continuous measurement records. We determine the dispersion of the speed of evolution and characterize the full statistics of single trajectories. By characterizing the dispersion of the Bures angle, we further show that continuous quantum measurements induce Brownian dynamics in Hilbert space.