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21.12.2015 | Foundations

Compatibility of observables on effect algebras

verfasst von: S. Pulmannová, E. Vinceková

Erschienen in: Soft Computing | Ausgabe 10/2016

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We compare different notions of simultaneous measurability (compatibility) of observables on lattice \(\sigma \)-effect algebras and more generally, on \(\sigma \)-effect algebras that can be covered by \(\sigma \)-MV-algebras. We prove that every \(\sigma \)-MV-algebra is the range of a \(\sigma \)-additive observable, and we compare the following notions of compatibility of observables: joint measurability, coexistence, joint measurability of binarizations, coexistence of binarizations, smearings of the same observable. We prove that if there is a faithful state on the effect algebra, then any two standard observables that are smearings of the same (sharp) observable admit a generalized joint observable.

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Titel: Compatibility of observables on effect algebras
verfasst von: S. Pulmannová
E. Vinceková
Publikationsdatum: 21.12.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 10/2016
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-015-1984-y

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