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Article: Optimal estimation of group transformations using entanglement

TitleOptimal estimation of group transformations using entanglement
Authors
Issue Date2005
Citation
Physical Review A - Atomic, Molecular, and Optical Physics, 2005, v. 72, n. 4 How to Cite?
AbstractWe derive the optimal input states and the optimal quantum measurements for estimating the unitary action of a given symmetry group, showing how the optimal performance is obtained with a suitable use of entanglement. Optimality is defined in a Bayesian sense, as minimization of the average value of a given cost function. We introduce a class of cost functions that generalizes the Holevo class for phase estimation, and show that for states of the optimal form all functions in such a class lead to the same optimal measurement. As a first application of the main result is the complete proof of the optimal efficiency in the transmission of a Cartesian reference frame. As a second application, we derive the optimal estimation of a completely unknown two-qubit maximally entangled state, provided that N copies of the state are available. In the limit of large N, the fidelity of the optimal estimation is shown to be 1-3/(4N). © 2005 The American Physical Society.
Persistent Identifierhttp://hdl.handle.net/10722/212845
ISSN
2014 Impact Factor: 2.808
2015 SCImago Journal Rankings: 1.418
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChiribella, G.-
dc.contributor.authorD'Ariano, G. M.-
dc.contributor.authorSacchi, M. F.-
dc.date.accessioned2015-07-28T04:05:12Z-
dc.date.available2015-07-28T04:05:12Z-
dc.date.issued2005-
dc.identifier.citationPhysical Review A - Atomic, Molecular, and Optical Physics, 2005, v. 72, n. 4-
dc.identifier.issn1050-2947-
dc.identifier.urihttp://hdl.handle.net/10722/212845-
dc.description.abstractWe derive the optimal input states and the optimal quantum measurements for estimating the unitary action of a given symmetry group, showing how the optimal performance is obtained with a suitable use of entanglement. Optimality is defined in a Bayesian sense, as minimization of the average value of a given cost function. We introduce a class of cost functions that generalizes the Holevo class for phase estimation, and show that for states of the optimal form all functions in such a class lead to the same optimal measurement. As a first application of the main result is the complete proof of the optimal efficiency in the transmission of a Cartesian reference frame. As a second application, we derive the optimal estimation of a completely unknown two-qubit maximally entangled state, provided that N copies of the state are available. In the limit of large N, the fidelity of the optimal estimation is shown to be 1-3/(4N). © 2005 The American Physical Society.-
dc.languageeng-
dc.relation.ispartofPhysical Review A - Atomic, Molecular, and Optical Physics-
dc.titleOptimal estimation of group transformations using entanglement-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1103/PhysRevA.72.042338-
dc.identifier.scopuseid_2-s2.0-28844480109-
dc.identifier.volume72-
dc.identifier.issue4-
dc.identifier.eissn1094-1622-
dc.identifier.isiWOS:000232931800072-

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