Characterization of informational completeness for covariant phase space observables

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dc.identifier.uri http://dx.doi.org/10.15488/8784
dc.identifier.uri https://www.repo.uni-hannover.de/handle/123456789/8837
dc.contributor.author Kiukas, J.
dc.contributor.author Lahti, P.
dc.contributor.author Schultz, J.
dc.contributor.author Werner, R.F.
dc.date.accessioned 2019-12-11T12:50:54Z
dc.date.available 2019-12-11T12:50:54Z
dc.date.issued 2012
dc.identifier.citation Kiukas, J.; Lahti, P.; Schultz, J.; Werner, R.F.: Characterization of informational completeness for covariant phase space observables. In: Journal of Mathematical Physics 53 (2012), Nr. 10, 102103. DOI: https://doi.org/10.1063/1.4754278
dc.description.abstract In the nonrelativistic setting with finitely many canonical degrees of freedom, a shift-covariant phase space observable is uniquely characterized by a positive operator of trace one and, in turn, by the Fourier-Weyl transform of this operator. We study three properties of such observables, and characterize them in terms of the zero set of this transform. The first is informational completeness, for which it is necessary and sufficient that the zero set has dense complement. The second is a version of informational completeness for the Hilbert-Schmidt class, equivalent to the zero set being of measure zero, and the third, known as regularity, is equivalent to the zero set being empty. We give examples demonstrating that all three conditions are distinct. The three conditions are the special cases for p = 1, 2, ∞ of a more general notion of p-regularity defined as the norm density of the span of translates of the operator in the Schatten-p class. We show that the relation between zero sets and p-regularity can be mapped completely to the corresponding relation for functions in classical harmonic analysisIn the nonrelativistic setting with finitely many canonical degrees of freedom, a shift-covariant phase space observable is uniquely characterized by a positive operator of trace one and, in turn, by the Fourier-Weyl transform of this operator. We study three properties of such observables, and characterize them in terms of the zero set of this transform. The first is informational completeness, for which it is necessary and sufficient that the zero set has dense complement. The second is a version of informational completeness for the Hilbert-Schmidt class, equivalent to the zero set being of measure zero, and the third, known as regularity, is equivalent to the zero set being empty. We give examples demonstrating that all three conditions are distinct. The three conditions are the special cases for p = 1, 2, ∞ of a more general notion of p-regularity defined as the norm density of the span of translates of the operator in the Schatten-p class. We show that the relation between zero sets and p-regularity can be mapped completely to the corresponding relation for functions in classical harmonic analysis eng
dc.language.iso eng
dc.publisher College Park, MD : American Institute of Physics
dc.relation.ispartofseries Journal of Mathematical Physics 53 (2012)
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
dc.subject Fourier-Weyl transform eng
dc.subject quantum mechanics eng
dc.subject Fourier transform eng
dc.subject.ddc 530 | Physik ger
dc.title Characterization of informational completeness for covariant phase space observables eng
dc.type article
dc.type Text
dc.relation.essn 1089-7658
dc.relation.issn 0022-2488
dc.relation.doi https://doi.org/10.1063/1.4754278
dc.bibliographicCitation.issue 10
dc.bibliographicCitation.volume 53
dc.bibliographicCitation.firstPage 102103
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


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