Structural characterization of linear quantum systems with application to back-action evading measurement

TL;DR

This paper analyzes the structure of quantum linear systems using the Kalman canonical form, revealing controllability and observability conditions, and introduces a new parameterization to simplify quantum control design, especially for back-action evading measurements.

Contribution

It proposes a novel parameterization method for quantum linear systems aligned with the Kalman canonical form, facilitating control design and realization of BAE measurements.

Findings

Quantum linear systems are controllable and observable if Hurwitz stable.

A new blockwise parameterization simplifies quantum control problems.

Conditions for realizing quantum BAE measurements are established.

Abstract

The purpose of this paper is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper \cite{ZGPG18}. The spectral structure of quantum linear systems is explored, which indicates that a quantum linear system is both controllable and observable provided that it is Hurwitz stable. A new parameterization method for quantum linear systems is proposed. This parameterization is designed for the Kalman canonical form directly. Consequently, the parameters involved are in a blockwise form in correspondence with the blockwise structure of the Kalman canonical form. This parameter structure can be used to simplify various quantum control design problems. For example, necessary and sufficient conditions for the realization of quantum back-action evading (BAE) measurements are given in terms of these new parameters. Due to their blockwise nature, a small number of parameters are required for realizing quantum BAE measurements.