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Open AccessArticle

Positive-Operator Valued Measure (POVM) Quantization

1
Astroparticules et Cosmologie (APC, UMR 7164), Université Paris 7-Paris Diderot, Sorbonne Paris Cité, 75205 Paris, France
2
Centro Brasileiro de Pesquisas Físicas, 22290-180 - Rio de Janeiro, RJ, Brazil
3
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
*
Author to whom correspondence should be addressed.
Academic Editor: James D. Malley
Axioms 2015, 4(1), 1-29; https://doi.org/10.3390/axioms4010001
Received: 3 September 2014 / Accepted: 18 December 2014 / Published: 25 December 2014
(This article belongs to the Special Issue Quantum Statistical Inference)
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on a normalized positive operator-valued measure. The latter are built from families of density operators labeled by points of the measure space. We especially focus on various probabilistic aspects of these constructions. Simple ormore elaborate examples illustrate the procedure: circle, two-sphere, plane and half-plane. Links with Positive-Operator Valued Measure (POVM) quantum measurement and quantum statistical inference are sketched. View Full-Text
Keywords: POVM; quantization; covariance; density operators; quantum measurement POVM; quantization; covariance; density operators; quantum measurement
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Gazeau, J.P.; Heller, B. Positive-Operator Valued Measure (POVM) Quantization. Axioms 2015, 4, 1-29.

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