dorsal/arxiv
View SchemaExtremal covariant measurements
| Authors | G. Chiribella, G. M. D'Ariano |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603168 |
| URL | https://arxiv.org/abs/quant-ph/0603168 |
| DOI | 10.1063/1.2349481 |
| Journal | J. Math. Phys. 47, 092107 (2006) |
Abstract
We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is generally non-transitive. In this case the POVM density is made of multiple orbits of positive operators, and, in the case of extremal measurements, we provide a bound for the number of orbits and for the rank of POVM elements. Two relevant applications are considered, concerning state discrimination with mutually unbiased bases and the maximization of the mutual information.
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"abstract": "We characterize the extremal points of the convex set of quantum measurements\nthat are covariant under a finite-dimensional projective representation of a\ncompact group, with action of the group on the measurement probability space\nwhich is generally non-transitive. In this case the POVM density is made of\nmultiple orbits of positive operators, and, in the case of extremal\nmeasurements, we provide a bound for the number of orbits and for the rank of\nPOVM elements. Two relevant applications are considered, concerning state\ndiscrimination with mutually unbiased bases and the maximization of the mutual\ninformation.",
"arxiv_id": "quant-ph/0603168",
"authors": [
"G. Chiribella",
"G. M. D\u0027Ariano"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2349481",
"journal_ref": "J. Math. Phys. 47, 092107 (2006)",
"title": "Extremal covariant measurements",
"url": "https://arxiv.org/abs/quant-ph/0603168"
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