Optimality of feedback control strategies for qubit purification
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Recently two papers [K. Jacobs, Phys. Rev. A 67, 030301(R) (2003); H. M. Wiseman and J. F. Ralph, New J. Physics 8, 90 (2006)] have derived a number of control strategies for rapid purification of qubits, optimized with respect to various goals. In the former paper the proof of optimality was not mathematically rigorous, while the latter gave only heuristic arguments for optimality. In this paper we provide rigorous proofs of optimality in all cases, by applying simple concepts from optimal control theory, including Bellman equations and verification theorems.
Quantum Information Processing
Copyright 2008 Springer-Verlag. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. The original publication is available at www.springerlink.com