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dc.contributor.authorNavascués, M.en_US
dc.contributor.authorFeix, A.en_US
dc.contributor.authorAraújo, M.en_US
dc.contributor.authorVértesi, T.en_US
dc.date.accessioned2016-02-08T11:03:35Z
dc.date.available2016-02-08T11:03:35Z
dc.date.issued2015en_US
dc.identifier.issn10502947
dc.identifier.urihttp://hdl.handle.net/11693/26696
dc.description.abstractWe study and extend the semidefinite programming (SDP) hierarchies introduced in Navascués and Vértesi [Phys. Rev. Lett. 115, 020501 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.020501] for the characterization of the statistical correlations arising from finite-dimensional quantum systems. First, we introduce the dimension-constrained noncommutative polynomial optimization (NPO) paradigm, where a number of polynomial inequalities are defined and optimization is conducted over all feasible operator representations of bounded dimensionality. Important problems in device-independent and semi-device-independent quantum information science can be formulated (or almost formulated) in this framework. We present effective SDP hierarchies to attack the general dimension-constrained NPO problem (and related ones) and prove their asymptotic convergence. To illustrate the power of these relaxations, we use them to derive a number of dimension witnesses for temporal and Bell-type correlation scenarios, and also to bound the probability of success of quantum random access codes. © 2015 American Physical Society.en_US
dc.language.isoEnglishen_US
dc.source.titlePhysical Review A - Atomic, Molecular, and Optical Physicsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevA.92.042117en_US
dc.subjectQuantum opticsen_US
dc.subjectAsymptotic convergenceen_US
dc.subjectFinite-dimensional quantum systemsen_US
dc.subjectNoncommutative polynomialsen_US
dc.subjectPolynomial inequalitiesen_US
dc.subjectProbability of successen_US
dc.subjectQuantum information scienceen_US
dc.subjectSemi-definite programmingen_US
dc.subjectStatistical correlationen_US
dc.subjectConstrained optimizationen_US
dc.titleCharacterizing finite-dimensional quantum behavioren_US
dc.typeArticleen_US
dc.departmentDepartment of Physicsen_US
dc.citation.volumeNumber92en_US
dc.citation.issueNumber4en_US
dc.identifier.doi10.1103/PhysRevA.92.042117en_US
dc.publisherAmerican Physical Societyen_US


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