Extreme Covariant Observables for Type I Symmetry Groups

: Holevo AS, Pellonpaa JP

Publisher: Springer

: 2009

: Foundations of Physics

: FOUNDATIONS OF PHYSICS

: FOUND PHYS

: 39

: 6

: 625

: 641

: 17

: 0015-9018

DOI: https://doi.org/10.1007/s10701-009-9274-0

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.