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Representation of probabilistic data by complex probability amplitudes: the case of triple-valued observables.PrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2010 (English)In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1327, p. 439-449Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Institute of Physics (AIP), 2010. Vol. 1327, p. 439-449
##### National Category

Mathematics
##### Research subject

Natural Science, Mathematics
##### Identifiers

URN: urn:nbn:se:lnu:diva-13821ISBN: 978-0-7354-0882-1 (print)OAI: oai:DiVA.org:lnu-13821DiVA, id: diva2:435378
##### Conference

International Conference Advances in Quantum Theory Location: Vaxjo, SWEDEN Date: JUN 14-17, 2010
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1130",{id:"formSmash:j_idt1130",widgetVar:"widget_formSmash_j_idt1130",multiple:true}); Available from: 2011-08-18 Created: 2011-08-18 Last updated: 2018-05-16Bibliographically approved
##### In thesis

The problem of inter-relation between classical and quantum probabilistic data wasdiscussed in numerous papers (from various points of view), see, e.g., [1, 2, 3, 4, 6, 5, 7,8, 14, 15]. We are interested in the problem of representation of probabilistic data of anyorigin 1 by complex probability amplitude, so to say a “wave function”. This problemwas discussed in very detail in [17]. A general QL-representation algorithm (QLRA)was presented in [17]. This algorithm is based on the formula of total probability withinterference term – a disturbance of the standard formula of total probability. Startingwith experimental probabilistic data, QLRA produces a complex probability amplitudesuch that probability can be reconstructed by using Born’s rule.Although the formal scheme of QLRA works for multi-valued observables of anarbitrary dimension, the description of the class of probabilistic data which can betransfered into QL-amplitudes (the domain of application of QLRA) depends very muchon the dimension. In [19] the simplest case of data generated by dichotomous observableswas studied. In this paper we study trichotomous observables. The complexity of theproblem increases incredibly comparing with the two dimensional case.Finally, we remark that our study is closely related to the triple slit interferenceexperiment and Sorkin’s equality [16]. This experiment provides an important test offoundations of QM.The scheme of presentation is the following one. We start with observables given byQM and derive constraints on phases which are necessary and sufficient for the QLrepresentation.Then we use these constraints to produce complex amplitudes from data(of any origin); some examples, including numerical, are given.

1. On relations between classical and quantum theories of information and probability$(function(){PrimeFaces.cw("OverlayPanel","overlay435435",{id:"formSmash:j_idt1404:0:j_idt1408",widgetVar:"overlay435435",target:"formSmash:j_idt1404:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
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