Observer-based quantum state estimation by continuous weak measurement

TL;DR

This paper introduces a novel quantum state estimation method using the Back and Forth Nudging approach, adapted from geophysical data assimilation, to improve initial state estimation in continuously measured quantum systems.

Contribution

It adapts the BFN method for quantum systems, providing a globally convergent estimator with proven convergence in the 2-level case and discussing extensions to multilevel systems.

Findings

The estimator converges asymptotically in the 2-level quantum system.

Simulation results support the convergence and effectiveness of the method.

Discussion on extending the approach to multilevel quantum systems.

Abstract

We propose to apply the Back and Forth Nudging (BFN) method used for geophysical data assimilations to estimate the initial state of a quantum system. We consider a cloud of atoms interacting with a magnetic field while a single observable is being continuously measured over time using homodyne detection. The BFN method relies on designing an observer forward and backwards in time. The state of the BFN observer is continuously updated by the measured data and tends to converge to the systems state. The proposed estimator seems to be globally asymptotically convergent when the system is observable. A detailed convergence proof and simulations are given in the 2-level case. A discussion on the extension of the algorithm to the multilevel case is also presented.