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Robust observer for uncertain linear quantum systems

Yamamoto, Naoki (2006) Robust observer for uncertain linear quantum systems. Physical Review A, 74 (3). Art. No. 032107. ISSN 1050-2947. doi:10.1103/PhysRevA.74.032107.

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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.

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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.
Subject Keywords:quantum theory; stochastic processes; differential equations; filtering theory; estimation theory
Issue or Number:3
Record Number:CaltechAUTHORS:YAMpra06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5653
Deposited By: Archive Administrator
Deposited On:27 Oct 2006
Last Modified:08 Nov 2021 20:27

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