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Article: Barycentric decomposition of quantum measurements in finite dimensions
Title | Barycentric decomposition of quantum measurements in finite dimensions |
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Authors | |
Issue Date | 2010 |
Citation | Journal of Mathematical Physics, 2010, v. 51, n. 2 How to Cite? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/213107 |
ISSN | 2015 Impact Factor: 1.234 2015 SCImago Journal Rankings: 0.767 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chiribella, Giulio | - |
dc.contributor.author | D'Ariano, Giacomo Mauro | - |
dc.contributor.author | Schlingemann, Dirk | - |
dc.date.accessioned | 2015-07-28T04:06:09Z | - |
dc.date.available | 2015-07-28T04:06:09Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Journal of Mathematical Physics, 2010, v. 51, n. 2 | - |
dc.identifier.issn | 0022-2488 | - |
dc.identifier.uri | http://hdl.handle.net/10722/213107 | - |
dc.description.abstract | We 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.language | eng | - |
dc.relation.ispartof | Journal of Mathematical Physics | - |
dc.title | Barycentric decomposition of quantum measurements in finite dimensions | - |
dc.type | Article | - |
dc.description.nature | Link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1063/1.3298681 | - |
dc.identifier.scopus | eid_2-s2.0-77952245067 | - |
dc.identifier.volume | 51 | - |
dc.identifier.issue | 2 | - |
dc.identifier.isi | WOS:000275032100011 | - |