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Article: Barycentric decomposition of quantum measurements in finite dimensions

TitleBarycentric decomposition of quantum measurements in finite dimensions
Authors
Issue Date2010
Citation
Journal of Mathematical Physics, 2010, v. 51, n. 2 How to Cite?
AbstractWe analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme points of the convex set are operator valued measures concentrated on a finite set of k ≤ d 2 points of the outcome space, d<∞ being the dimension of the Hilbert space. We prove that for second-countable outcome spaces any POVM admits a Choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure. In the general case, Krein-Milman theorem is invoked to represent POVMs as barycenters of a certain set of POVMs concentrated on k ≤ d 2 points of the outcome space. © 2010 American Institute of Physics.
Persistent Identifierhttp://hdl.handle.net/10722/213107
ISSN
2015 Impact Factor: 1.234
2015 SCImago Journal Rankings: 0.767
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChiribella, Giulio-
dc.contributor.authorD'Ariano, Giacomo Mauro-
dc.contributor.authorSchlingemann, Dirk-
dc.date.accessioned2015-07-28T04:06:09Z-
dc.date.available2015-07-28T04:06:09Z-
dc.date.issued2010-
dc.identifier.citationJournal of Mathematical Physics, 2010, v. 51, n. 2-
dc.identifier.issn0022-2488-
dc.identifier.urihttp://hdl.handle.net/10722/213107-
dc.description.abstractWe analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme points of the convex set are operator valued measures concentrated on a finite set of k ≤ d 2 points of the outcome space, d<∞ being the dimension of the Hilbert space. We prove that for second-countable outcome spaces any POVM admits a Choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure. In the general case, Krein-Milman theorem is invoked to represent POVMs as barycenters of a certain set of POVMs concentrated on k ≤ d 2 points of the outcome space. © 2010 American Institute of Physics.-
dc.languageeng-
dc.relation.ispartofJournal of Mathematical Physics-
dc.titleBarycentric decomposition of quantum measurements in finite dimensions-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1063/1.3298681-
dc.identifier.scopuseid_2-s2.0-77952245067-
dc.identifier.volume51-
dc.identifier.issue2-
dc.identifier.isiWOS:000275032100011-

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