Single shot parameter estimation via continuous quantum measurement

TL;DR

This paper introduces a quantum filtering approach for single shot parameter estimation using continuous measurement, providing optimal Bayesian filters for finite parameters and quantum particle filters for continuous parameters, with convergence analysis.

Contribution

It develops a unified quantum filtering framework for parameter estimation, including practical quantum particle filters and convergence conditions.

Findings

Derived optimal Bayesian filters for finite parameter ranges

Developed quantum particle filters for continuous parameters

Provided convergence conditions for the estimators

Abstract

We present filtering equations for single shot parameter estimation using continuous quantum measurement. By embedding parameter estimation in the standard quantum filtering formalism, we derive the optimal Bayesian filter for cases when the parameter takes on a finite range of values. Leveraging recent convergence results [van Handel, arXiv:0709.2216 (2008)], we give a condition which determines the asymptotic convergence of the estimator. For cases when the parameter is continuous valued, we develop quantum particle filters as a practical computational method for quantum parameter estimation.