Estimation of classical parameters via continuous probing of complementary quantum observables

TL;DR

This paper presents a Bayesian filtering approach for estimating unknown classical parameters, such as magnetic field direction, by continuously probing a quantum system and analyzing the resulting measurement data.

Contribution

It generalizes the stochastic master equation to a Bayesian filter for parameter estimation in quantum systems, demonstrated through magnetic field direction estimation.

Findings

Effective Bayesian filtering for quantum parameter estimation.

Successful estimation of magnetic field direction from optical measurements.

Framework applicable to various quantum sensing scenarios.

Abstract

We discuss how continuous probing of a quantum system allows estimation of unknown classical parameters embodied in the Hamiltonian of the system. We generalize the stochastic master equation associated with continuous observation processes to a Bayesian filter equation for the probability distribution of the desired parameters, and we illustrate its application by estimating the direction of a magnetic field. In our example, the field causes a ground state spin precession in a two-level atom which is detected by the polarization rotation of off-resonant optical probes, interacting with the atomic spin components.