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Stabilizing Feedback Controls for Quantum Systems

Mirrahimi, Mazyar and van Handel, Ramon (2007) Stabilizing Feedback Controls for Quantum Systems. SIAM Journal on Control and Optimization, 46 (2). pp. 445-467. ISSN 0363-0129.

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No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is necessarily one with partial observations and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory. Here we study the properties of controlled quantum filtering equations as classical stochastic differential equations. We then develop methods, using a combination of geometric control and classical probabilistic techniques, for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator.

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Additional Information:©2007 Society for Industrial and Applied Mathematics Received by the editors November 10, 2005; accepted for publication (in revised form) October 22, 2006; published electronically April 27, 2007. This work was supported by the ARO under grant DAAD19-03-1-0073. The authors thank Hideo Mabuchi and Houman Owhadi for helpful discussions.
Subject Keywords:quantum feedback control, quantum filtering equations, stochastic stabilization
Issue or Number:2
Record Number:CaltechAUTHORS:MIRsiamjco07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8423
Deposited By: Archive Administrator
Deposited On:03 Aug 2007
Last Modified:02 Oct 2019 23:50

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