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Article: Optimal quantum learning of a unitary transformation

TitleOptimal quantum learning of a unitary transformation
Authors
Issue Date2010
Citation
Physical Review A - Atomic, Molecular, and Optical Physics, 2010, v. 81, n. 3 How to Cite?
AbstractWe address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary with maximum fidelity. Learning a unitary is equivalent to storing it in the state of a quantum memory (the memory of the learning machine) and subsequently retrieving it. We prove that, whenever the unknown unitary is drawn from a group, the optimal strategy consists in a parallel call of the available uses followed by a "measure-and-rotate" retrieving. Differing from the case of quantum cloning, where the incoherent "measure-and-prepare" strategies are typically suboptimal, in the case of learning the "measure-and-rotate" strategy is optimal even when the learning machine is asked to reproduce a single copy of the unknown unitary. We finally address the problem of the optimal inversion of an unknown unitary evolution, showing also in this case the optimality of the "measure-and-rotate" strategies and applying our result to the optimal approximate realignment of reference frames for quantum communication. © 2010 The American Physical Society.
Persistent Identifierhttp://hdl.handle.net/10722/213100
ISSN
2014 Impact Factor: 2.808
2015 SCImago Journal Rankings: 1.418
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorBisio, Alessandro-
dc.contributor.authorChiribella, Giulio-
dc.contributor.authorD'Ariano, Giacomo Mauro-
dc.contributor.authorFacchini, Stefano-
dc.contributor.authorPerinotti, Paolo-
dc.date.accessioned2015-07-28T04:06:08Z-
dc.date.available2015-07-28T04:06:08Z-
dc.date.issued2010-
dc.identifier.citationPhysical Review A - Atomic, Molecular, and Optical Physics, 2010, v. 81, n. 3-
dc.identifier.issn1050-2947-
dc.identifier.urihttp://hdl.handle.net/10722/213100-
dc.description.abstractWe address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary with maximum fidelity. Learning a unitary is equivalent to storing it in the state of a quantum memory (the memory of the learning machine) and subsequently retrieving it. We prove that, whenever the unknown unitary is drawn from a group, the optimal strategy consists in a parallel call of the available uses followed by a "measure-and-rotate" retrieving. Differing from the case of quantum cloning, where the incoherent "measure-and-prepare" strategies are typically suboptimal, in the case of learning the "measure-and-rotate" strategy is optimal even when the learning machine is asked to reproduce a single copy of the unknown unitary. We finally address the problem of the optimal inversion of an unknown unitary evolution, showing also in this case the optimality of the "measure-and-rotate" strategies and applying our result to the optimal approximate realignment of reference frames for quantum communication. © 2010 The American Physical Society.-
dc.languageeng-
dc.relation.ispartofPhysical Review A - Atomic, Molecular, and Optical Physics-
dc.titleOptimal quantum learning of a unitary transformation-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1103/PhysRevA.81.032324-
dc.identifier.scopuseid_2-s2.0-77949954278-
dc.identifier.volume81-
dc.identifier.issue3-
dc.identifier.eissn1094-1622-
dc.identifier.isiWOS:000276262500073-

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