TY - JOUR

T1 - Robust observer for uncertain linear quantum systems

AU - Yamamoto, Naoki

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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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U2 - 10.1103/PhysRevA.74.032107

DO - 10.1103/PhysRevA.74.032107

M3 - Article

AN - SCOPUS:33748975146

VL - 74

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 032107

ER -