A1 Refereed original research article in a scientific journal
Extreme covariant quantum observables in the case of an Abelian symmetry group and a transitive value space
Authors: Haapasalo ET, Pellonpaa JP
Publisher: AMER INST PHYSICS
Publication year: 2011
Journal: Journal of Mathematical Physics
Journal name in source: JOURNAL OF MATHEMATICAL PHYSICS
Journal acronym: J MATH PHYS
Article number: ARTN 122102
Number in series: 12
Volume: 52
Issue: 12
Number of pages: 23
ISSN: 0022-2488
DOI: https://doi.org/10.1063/1.3668317
Self-archived copy’s web address: https://arxiv.org/abs/1105.1084
Abstract
We represent quantum observables as normalized positive operator valued measures and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group G. The value space of such observables is a transitive G-space. We characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables. The results are applied to position, position difference, and time observables. (C) 2011 American Institute of Physics. [doi:10.1063/1.3668317]
We represent quantum observables as normalized positive operator valued measures and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group G. The value space of such observables is a transitive G-space. We characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables. The results are applied to position, position difference, and time observables. (C) 2011 American Institute of Physics. [doi:10.1063/1.3668317]
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