On estimation and feedback control of spin-1/2 systems with unknown initial states

TL;DR

This paper investigates the asymptotic convergence of quantum filters for spin-1/2 systems under feedback control with unknown initial states and measurement imperfections, demonstrating filter fidelity convergence and discussing stabilization for higher spins.

Contribution

It proves the convergence of quantum filters in spin-1/2 systems with unknown initial states and measurement imperfections, and discusses stabilization strategies for spin-J systems.

Findings

Fidelity between actual and estimated filters converges to one.

Asymptotic behavior of filters discussed for spin-J systems.

Potential for exponential stabilization towards eigenvectors.

Abstract

In this paper, we consider stochastic master equations describing the evolutions of quantum systems interacting with electromagnetic fields undergoing continuous-time measurements. In particular, we study feedback control of quantum spin-1/2 systems in the case of unawareness of initial states and in presence of measurement imperfections. We prove that the fidelity between the actual quantum filter and its associated estimated filter converges to one under appropriate assumption on the feedback controller. This shows the asymptotic convergence of such filters. In addition, for spin-J systems, we discuss heuristically the asymptotic behavior of the actual quantum filter and its associated estimated filter and the possibility of exponentially stabilizing such systems towards an eigenvector of the measurement operator by an appropriate feedback.