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Extreme covariant quantum observables in the case of an Abelian symmetry group and a transitive value space
Tekijät: Haapasalo ET, Pellonpaa JP
Kustantaja: AMER INST PHYSICS
Julkaisuvuosi: 2011
Journal: Journal of Mathematical Physics
Tietokannassa oleva lehden nimi: JOURNAL OF MATHEMATICAL PHYSICS
Lehden akronyymi: J MATH PHYS
Artikkelin numero: ARTN 122102
Numero sarjassa: 12
Vuosikerta: 52
Numero: 12
Sivujen määrä: 23
ISSN: 0022-2488
DOI: https://doi.org/10.1063/1.3668317
Rinnakkaistallenteen osoite: https://arxiv.org/abs/1105.1084
Tiivistelmä
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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