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Extreme Covariant Observables for Type I Symmetry Groups
Tekijät: Holevo AS, Pellonpaa JP
Kustantaja: Springer
Julkaisuvuosi: 2009
Journal: Foundations of Physics
Tietokannassa oleva lehden nimi: FOUNDATIONS OF PHYSICS
Lehden akronyymi: FOUND PHYS
Vuosikerta: 39
Numero: 6
Aloitussivu: 625
Lopetussivu: 641
Sivujen määrä: 17
ISSN: 0015-9018
DOI: https://doi.org/10.1007/s10701-009-9274-0
Tiivistelmä
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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