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Article: Optimal estimation of group transformations using entanglement

TitleOptimal estimation of group transformations using entanglement
Authors
Issue Date2005
PublisherAmerican Physical Society. The Journal's web site is located at http://journals.aps.org/pra/
Citation
Physical Review A (Atomic, Molecular and Optical Physics), 2005, v. 72 n. 4, article no. 042338 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, article no. 042338-
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.publisherAmerican Physical Society. The Journal's web site is located at http://journals.aps.org/pra/-
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.spagearticle no. 042338-
dc.identifier.epagearticle no. 042338-
dc.identifier.eissn1094-1622-
dc.identifier.isiWOS:000232931800072-

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