### 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.

Original language | English |
---|---|

Article number | 032107 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 74 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2006 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)

### Cite this

**Robust observer for uncertain linear quantum systems.** / Yamamoto, Naoki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Robust observer for uncertain linear quantum systems

AU - Yamamoto, Naoki

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.

UR - http://www.scopus.com/inward/record.url?scp=33748975146&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748975146&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.74.032107

DO - 10.1103/PhysRevA.74.032107

M3 - Article

VL - 74

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

M1 - 032107

ER -