dorsal/arxiv
View SchemaClean Positive Operator Valued Measures
| Authors | F. Buscemi, G. M. D'Ariano, M. Keyl, P. Perinotti, R. Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505095 |
| URL | https://arxiv.org/abs/quant-ph/0505095 |
| DOI | 10.1063/1.2008996 |
| Journal | J. Math. Phys. 46, 082109 (2005) |
Abstract
In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVM's into POVM's, generally irreversibly, thus loosing some of the information retrieved from the measurement. This poses the problem of which POVM's are "undisturbed", namely they are not irreversibly connected to another POVM. We will call such POVM clean. In a sense, the clean POVM's would be "perfect", since they would not have any additional "extrinsical" noise. Quite unexpectedly, it turns out that such cleanness property is largely unrelated to the convex structure of POVM's, and there are clean POVM's that are not extremal and vice-versa. In this paper we solve the cleannes classification problem for number n of outcomes n<=d (d dimension of the Hilbert space), and we provide a a set of either necessary or sufficient conditions for n>d, along with an iff condition for the case of informationally complete POVM's for n=d^2.
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"abstract": "In quantum mechanics the statistics of the outcomes of a measuring apparatus\nis described by a positive operator valued measure (POVM). A quantum channel\ntransforms POVM\u0027s into POVM\u0027s, generally irreversibly, thus loosing some of the\ninformation retrieved from the measurement. This poses the problem of which\nPOVM\u0027s are \"undisturbed\", namely they are not irreversibly connected to another\nPOVM. We will call such POVM clean. In a sense, the clean POVM\u0027s would be\n\"perfect\", since they would not have any additional \"extrinsical\" noise. Quite\nunexpectedly, it turns out that such cleanness property is largely unrelated to\nthe convex structure of POVM\u0027s, and there are clean POVM\u0027s that are not\nextremal and vice-versa. In this paper we solve the cleannes classification\nproblem for number n of outcomes n\u003c=d (d dimension of the Hilbert space), and\nwe provide a a set of either necessary or sufficient conditions for n\u003ed, along\nwith an iff condition for the case of informationally complete POVM\u0027s for\nn=d^2.",
"arxiv_id": "quant-ph/0505095",
"authors": [
"F. Buscemi",
"G. M. D\u0027Ariano",
"M. Keyl",
"P. Perinotti",
"R. Werner"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2008996",
"journal_ref": "J. Math. Phys. 46, 082109 (2005)",
"title": "Clean Positive Operator Valued Measures",
"url": "https://arxiv.org/abs/quant-ph/0505095"
},
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