Extreme Covariant Quantum Observables in the Case of an Abelian Symmetry Group and a Transitive Value Space

Details Extreme Covariant Quantum Observables in the Case of an Abelian Symmetry Group and a Transitive Value Space Extreme Covariant Quantum Observables in the Case of an Abelian Symmetry Group and a Transitive Value Space

2011-05-05

arxiv.org/abs/1105.1084v1

J. Math. Phys. 52, 122102 (2011)

Physics

Quantum Physics

23 pages

Scientific paper

We represent quantum observables as POVMs (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.

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