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Article: Optimal quantum learning of a unitary transformation
Title | Optimal quantum learning of a unitary transformation |
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Authors | |
Issue Date | 2010 |
Citation | Physical Review A - Atomic, Molecular, and Optical Physics, 2010, v. 81, n. 3 How to Cite? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/213100 |
ISSN | 2014 Impact Factor: 2.808 2015 SCImago Journal Rankings: 1.418 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bisio, Alessandro | - |
dc.contributor.author | Chiribella, Giulio | - |
dc.contributor.author | D'Ariano, Giacomo Mauro | - |
dc.contributor.author | Facchini, Stefano | - |
dc.contributor.author | Perinotti, Paolo | - |
dc.date.accessioned | 2015-07-28T04:06:08Z | - |
dc.date.available | 2015-07-28T04:06:08Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Physical Review A - Atomic, Molecular, and Optical Physics, 2010, v. 81, n. 3 | - |
dc.identifier.issn | 1050-2947 | - |
dc.identifier.uri | http://hdl.handle.net/10722/213100 | - |
dc.description.abstract | We 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.language | eng | - |
dc.relation.ispartof | Physical Review A - Atomic, Molecular, and Optical Physics | - |
dc.title | Optimal quantum learning of a unitary transformation | - |
dc.type | Article | - |
dc.description.nature | Link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1103/PhysRevA.81.032324 | - |
dc.identifier.scopus | eid_2-s2.0-77949954278 | - |
dc.identifier.volume | 81 | - |
dc.identifier.issue | 3 | - |
dc.identifier.eissn | 1094-1622 | - |
dc.identifier.isi | WOS:000276262500073 | - |