Positive-Operator Valued Measure (POVM) Quantization

Axioms

Jean Pierre Gazeau¹  Barbara Heller² 

[1] Astroparticules et Cosmologie (APC, UMR 7164), Université Paris 7-Paris Diderot, Sorbonne Paris Cité, 75205 Paris, France;Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA; E-Mail:

关键词: POVM;    quantization;    covariance;    density operators;    quantum measurement;   

DOI  :  10.3390/axioms4010001

来源: mdpi

【 摘 要 】

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 or more 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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.