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Published September 1, 2006 | public
Journal Article Open

Robust observer for uncertain linear quantum systems

Abstract

In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although in the linear case much of classical control theory can be applied to quantum systems, the quantum robust observer obtained in this paper does not have a classical analog due to the system's specific structure with respect to the uncertainties. Moreover, by considering a typical quantum control problem, we show that the proposed robust observer is fairly robust against a parametric uncertainty of the system even when the other estimators—the optimal Kalman filter and risk-sensitive observer—fail in the estimation.

Additional Information

©2006 The American Physical Society (Received 29 May 2006; revised 31 July 2006; published 21 September 2006) The author wishes to thank R. van Handel, L. Bouten, and H. Mabuchi for their helpful comments. This work was supported in part by the Grants-in-Aid for JSPS fellows Grant No. 06693.

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August 22, 2023
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