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arXiv:2209.03703 · Quantum Information Processing

On quantum channels generated by covariant positive operator-valued measures on a locally compact group

Grigori Gennadievich Amosov

Published Sep 17, 2022• 6 citations
arXivHTMLPDF
DOI
10.1007/s11128-022-03655-x

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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.