Zooming in on Quantum Trajectories

TL;DR

This paper introduces a novel approach to analyze quantum system evolution by redefining time based on measurement effects, revealing detailed dynamics and anomalous observables during quantum jumps.

Contribution

It presents a new effective time framework for studying monitored quantum systems, providing clear evolution equations and insights into quantum jumps and entropy dynamics.

Findings

Effective time reveals internal details of quantum jumps.

Anomalous localized observables are identified during sharp transitions.

Evolution of effective time relates to a stable Levy process of index 1/2.

Abstract

We propose to use the effect of measurements instead of their number to study the time evolution of quantum systems under monitoring. This time redefinition acts like a microscope which blows up the inner details of seemingly instantaneous transitions like quantum jumps. In the simple example of a continuously monitored qubit coupled to a heat bath, we show that this procedure provides well defined and simple evolution equations in an otherwise singular strong monitoring limit. We show that there exists anomalous observable localised on sharp transitions which can only be resolved with our new effective time. We apply our simplified description to study the competition between information extraction and dissipation in the evolution of the linear entropy. Finally, we show that the evolution of the new time as a function of the real time is closely related to a stable Levy process of index 1/2.