A1 Refereed original research article in a scientific journal
Extreme Covariant Observables for Type I Symmetry Groups
Authors: Holevo AS, Pellonpaa JP
Publisher: Springer
Publication year: 2009
Journal: Foundations of Physics
Journal name in source: FOUNDATIONS OF PHYSICS
Journal acronym: FOUND PHYS
Volume: 39
Issue: 6
First page : 625
Last page: 641
Number of pages: 17
ISSN: 0015-9018
DOI: https://doi.org/10.1007/s10701-009-9274-0
Abstract
The structure of covariant observables-normalized positive operator measures (POMs)-is studied in the case of a type I symmetry group. Such measures are completely determined by kernels which are measurable fields of positive semidefinite sesquilinear forms. We produce the minimal Kolmogorov decompositions for the kernels and determine those which correspond to the extreme covariant observables. Illustrative examples of the extremals in the case of the Abelian symmetry group are given.
The structure of covariant observables-normalized positive operator measures (POMs)-is studied in the case of a type I symmetry group. Such measures are completely determined by kernels which are measurable fields of positive semidefinite sesquilinear forms. We produce the minimal Kolmogorov decompositions for the kernels and determine those which correspond to the extreme covariant observables. Illustrative examples of the extremals in the case of the Abelian symmetry group are given.
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