Exponential Selection and Feedback Stabilization of Invariant Subspaces of Quantum Trajectories

TL;DR

This paper demonstrates that quantum trajectories rapidly converge to invariant subspaces with exponential speed, and introduces a feedback control method to target specific subspaces efficiently.

Contribution

It provides a novel proof of exponential convergence of quantum trajectories and develops a feedback control strategy for targeted subspace stabilization.

Findings

Quantum trajectories exponentially supported by invariant subspaces.

Lyapunov techniques used to prove convergence.

Feedback control achieves targeted subspace stabilization.

Abstract

We show that quantum trajectories become exponentially fast supported by one of their minimal invariant subspaces. Exponential convergence is shown in expectation using Lyapunov techniques. The proof is based on an in-depth study of the identifiability of the probability distributions generated in the different subspaces. We furthermore introduce a feedback control strategy that allows for the targeted convergence towards a desired subspace. This convergence is also achieved at exponential speed.