Optimality of feedback control strategies for qubit purification
Howard M. Wiseman, Luc Bouten
TL;DR
This paper rigorously proves the optimality of feedback control strategies for rapid qubit purification, using optimal control theory to validate previous heuristic and non-rigorous results.
Contribution
It provides the first rigorous proofs of optimal feedback control strategies for qubit purification, confirming earlier heuristic and non-rigorous findings.
Findings
Rigorous proofs of optimality for qubit purification strategies
Application of Bellman equations and verification theorems
Confirmation of previous heuristic control strategies
Abstract
Recently two papers [K. Jacobs, Phys. Rev. A {\bf 67}, 030301(R) (2003); H. M. Wiseman and J. F. Ralph, New J. Physics {\bf 8}, 90 (2006)] have derived 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.
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Taxonomy
TopicsQuantum Mechanics and Applications · Quantum Computing Algorithms and Architecture · Quantum Information and Cryptography