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arXiv:1309.0578 · Australian Control Conference

Coherent-classical estimation for quantum linear systems

Ian R. Petersen

Published Nov 1, 2013• 6 citations
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Abstract

This paper introduces a problem of coherent-classical estimation for a class of linear quantum systems. In this problem, the estimator is a mixed quantum-classical system which produces a classical estimate of a system variable. The coherent-classical estimator may also involve coherent feedback. An example involving optical squeezers is given to illustrate the efficacy of this idea.

DOI
10.1109/aucc.2013.6697322

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This paper introduces a problem of coherent-classical estimation for a class of linear quantum systems. In this problem, the estimator is a mixed quantum-classical system which produces a classical estimate of a system variable. The coherent-classical estimator may also involve coherent feedback. An example involving optical squeezers is given to illustrate the efficacy of this idea.
We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comprises an estimator that is a mixed quantum-classical system without involving coherent feedback. The estimator yields a classical estimate of a variable for the quantum plant. We demonstrate that for a passive plant that can be characterized by annihilation operators only, such coherent-classical estimation provides no improvement over purely-classical estimation. An example is also given which shows that if the plant is not assumed to be an annihilation operator only quantum system, it is possible to get better estimates with such coherent-classical estimation compared with purely-classical estimation.
We study robust H∞coherent-classical estimation for a class of physically realizable linear quantum systems with parameter uncertainties. Such a robust coherent-classical estimator, with or without coherent feedback, can yield better disturbance-to-error performance than the corresponding robust purely-classical estimator for an uncertain plant. Moreover, coherent feedback allows for such a robust coherent-classical estimator to be more robust to uncertainty in comparison to the robust classical-only estimator.
Robust H∞H_\inftyH∞​ Coherent-Classical Estimation.
We study robust H∞H_\inftyH∞​ coherent-classical estimation for a class of physically realizable linear quantum systems with parameter uncertainties. Such a robust coherent-classical estimator, with or without coherent feedback, can yield better disturbance-to-error performance than the corresponding robust purely-classical estimator for an uncertain plant. Moreover, coherent feedback allows for such a robust coherent-classical estimator to be more robust to uncertainty in comparison to the robust classical-only estimator.
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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∞ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled H∞ 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. Copyright © 2016 John Wiley & Sons, Ltd.