Absolute continuity for operator valued completely positive maps on C *-algebras

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dc.citation.epage022102-29en_US
dc.citation.issueNumber2en_US
dc.citation.spage022102-1en_US
dc.citation.volumeNumber50en_US
dc.contributor.authorGheondea, A.en_US
dc.contributor.authorKavruk, A. Ş.en_US
dc.date.accessioned2016-02-08T10:04:57Z
dc.date.available2016-02-08T10:04:57Z
dc.date.issued2009en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractMotivated by applicability to quantum operations, quantum information, and quantum probability, we investigate the notion of absolute continuity for operator valued completely positive maps on C* -algebras, previously introduced by Parthasarathy [in Athens Conference on Applied Probability and Time Series Analysis I (Springer-Verlag, Berlin, 1996), pp. 34-54]. We obtain an intrinsic definition of absolute continuity, we show that the Lebesgue decomposition defined by Parthasarathy is the maximal one among all other Lebesgue-type decompositions and that this maximal Lebesgue decomposition does not depend on the jointly dominating completely positive map, we obtain more flexible formulas for calculating the maximal Lebesgue decomposition, and we point out the nonuniqueness of the Lebesgue decomposition as well as a sufficient condition for uniqueness. In addition, we consider Radon-Nikodym derivatives for absolutely continuous completely positive maps that, in general, are unbounded positive self-adjoint operators affiliated to a certain von Neumann algebra, and we obtain a spectral approximation by bounded Radon-Nikodym derivatives. An application to the existence of the infimum of two completely positive maps is indicated, and formulas in terms of Choi's matrices for the Lebesgue decomposition of completely positive maps in matrix algebras are obtained. © 2009 American Institute of Physics.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T10:04:57Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2009en
dc.identifier.doi10.1063/1.3072683en_US
dc.identifier.eissn1089-7658
dc.identifier.issn0022-2488
dc.identifier.urihttp://hdl.handle.net/11693/22807
dc.language.isoEnglishen_US
dc.relation.isversionofhttp://dx.doi.org/10.1063/1.3072683en_US
dc.source.titleJournal of Mathematical Physicsen_US
dc.titleAbsolute continuity for operator valued completely positive maps on C *-algebrasen_US
dc.typeArticleen_US

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