Show simple item record

dc.contributor.authorVourdas, Apostolos*
dc.date.accessioned2016-01-08T15:35:03Z
dc.date.available2016-01-08T15:35:03Z
dc.date.issued2014-08
dc.identifier.citationVourdas A (2015) Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces. Journal of Mathematical Physics, 55(8): 082107.en_US
dc.identifier.urihttp://hdl.handle.net/10454/7647
dc.descriptionyesen_US
dc.description.abstractThe orthocomplemented modular lattice of subspaces L[H(d)] , of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)] ). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H1,H2) , which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H1),P(H2) , to the subspaces H 1, H 2. As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities.en_US
dc.language.isoenen_US
dc.relation.isreferencedbyhttp://dx.doi.org/10.1063/1.4891972en_US
dc.rights© 2014 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in the Journal of Mathematical Physics and may be found at http://dx.doi.org/10.1063/1.4891972.en_US
dc.subjectQuantum probabilities; Dempster-Shafer probabilities; Hilbert space; Probability theory; Inequalities; Noncommutative field theoryen_US
dc.titleQuantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces.en_US
dc.status.refereedyesen_US
dc.date.Accepted2014-07-21
dc.typeArticleen_US
dc.type.versionAccepted Manuscripten_US
refterms.dateFOA2018-07-25T13:53:40Z


Item file(s)

Thumbnail
Name:
JMP2014.pdf
Size:
261.4Kb
Format:
PDF

This item appears in the following Collection(s)

Show simple item record