Identification and Estimation of Quantum Linear Input-Output Systems

TL;DR

This paper explores methods for identifying and estimating parameters of quantum linear systems from output measurements, addressing the fundamental questions of identifiability, system realization, and estimation accuracy under different input conditions.

Contribution

It provides a comprehensive analysis of parameter identifiability, system realization, and estimation techniques for quantum linear systems using both time-dependent and stationary inputs.

Findings

Parameters identifiable from output measurements are characterized.

Procedures for constructing system realizations from input-output data are developed.

Estimation accuracy bounds are established for quantum linear systems.

Abstract

The system identification problem is to estimate dynamical parameters from the output data, obtained by performing measurements on the output fields. We investigate system identification for quantum linear systems. Our main objectives are to address the following general problems: (1) Which parameters can be identified by measuring the output? (2) How can we construct a system realisation from sufficient input-output data? (3) How well can we estimate the parameters governing the dynamics? We investigate these problems in two contrasting approaches; using time-dependent inputs or time-stationary (quantum noise) inputs.