Measurement induced faster symmetry restoration in quantum trajectories

TL;DR

This paper demonstrates that continuous measurement back-action can be used as a resource to accelerate the restoration of a global U(1) symmetry in quantum systems, with the speed depending on the measurement protocol and initial state.

Contribution

It introduces a method to harness measurement back-action for faster symmetry restoration and shows its universality across protocols and initial states.

Findings

Global monitoring restores symmetry faster for distant charge sectors.

Local monitoring can further accelerate symmetry restoration.

Symmetry restoration speed depends on measurement protocol and initial state.

Abstract

Continuous measurement of quantum systems provides a standard route to quantum trajectories through the successive acquisition of information which further results in measurement back-action. In this work, we harness this back-action as a resource for global $U(1)$ symmetry restoration where continuous measurement is combined with a $U(1)$-preserving unitary evolution. Starting from a $U(1)$ symmetry-broken initial state, we simulate quantum trajectories generated by continuous measurements of both global and local observables. We show that under global monitoring, states containing superpositions of distant charge sectors restore symmetry faster than those involving nearby sectors. We establish the universality of this behavior across different measurement protocols. Finally, we demonstrate that local monitoring can further accelerate symmetry restoration for certain states that relax slowly under global monitoring.