Extreme covariant quantum observables in the case of an Abelian symmetry group and a transitive value space



: Haapasalo ET, Pellonpaa JP

Publisher: AMER INST PHYSICS

: 2011

: Journal of Mathematical Physics

: JOURNAL OF MATHEMATICAL PHYSICS

: J MATH PHYS

: ARTN 122102

: 12

: 52

: 12

: 23

: 0022-2488

DOI: https://doi.org/10.1063/1.3668317

: https://arxiv.org/abs/1105.1084


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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