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Extreme Covariant Observables for Type I Symmetry Groups |
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| Authors: | Alexander?S?Holevo Juha-Pekka?Pellonp?? |
| Institution: | (1) Department of Probability Theory, Steklov Mathematical Institute, Gubkina 8, 119991 Moscow, Russia;(2) Department of Physics, University of Turku, 20014 Turku, Finland |
| 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. Dedicated to Pekka J. Lahti in honor of his sixtieth birthday |
| Keywords: | Positive operator measure Generalized imprimitivity system Covariance system Covariant observable Extreme point Kolmogorov decomposition Measurable field of sesquilinear forms |
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