Asymptotic inference in system identification for the atom maser

TL;DR

This paper investigates asymptotic statistical methods for system identification in quantum systems, specifically estimating the Rabi frequency of an atom maser through continuous measurements, and establishes foundational theoretical results.

Contribution

It introduces a framework for asymptotic inference in quantum system identification, computing Fisher information and proving local asymptotic normality for the atom maser.

Findings

Computed Fisher information for various measurement processes

Established local asymptotic normality of the models

Connected spectral properties of deformed Markov generators to statistical inference

Abstract

System identification is an integrant part of control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However for quantum dynamical systems like quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input which may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators and the connection to large deviations is briefly discussed.