Robust $H_\infty$ Estimation of Uncertain Linear Quantum Systems

TL;DR

This paper develops a robust $H_ abla$ estimation method for uncertain linear quantum systems, transforming the problem into a scaled $H_ abla$ control problem and solving it via algebraic Riccati equations, with applications to dynamic squeezers.

Contribution

It introduces a novel robust $H_ abla$ estimation approach for uncertain quantum systems, extending previous work on optimal estimators to handle uncertainties.

Findings

The method effectively estimates uncertain quantum systems.

Solutions are obtained through algebraic Riccati equations.

Examples demonstrate the approach's effectiveness in dynamic squeezers.

Abstract

We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust $H_\infty$ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled $H_\infty$ control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method.