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On the consistency of the quantum-like representation algorithm for hyperbolic interference.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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2011 (English)In: Advances in Applied Clifford Algebras, ISSN 1661-4909, Vol. 21, no 4, p. 799-811Article in journal (Refereed) Published
##### Abstract [en]

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

2011. Vol. 21, no 4, p. 799-811
##### Keywords [en]

Born’s rule problem, hyperbolic interference, hyper trigonometric interference, inverse order of conditioning, quantum-like representation algorithm.
##### National Category

Mathematics
##### Research subject

Natural Science, Mathematics
##### Identifiers

URN: urn:nbn:se:lnu:diva-13820DOI: 10.1007/s00006-011-0287-3Scopus ID: 2-s2.0-80455173631OAI: oai:DiVA.org:lnu-13820DiVA, id: diva2:435369
#####

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##### Note

Online First™, 16 March 2011Available from: 2011-08-18 Created: 2011-08-18 Last updated: 2012-01-13Bibliographically approved
##### In thesis

Recently quantum-like representation algorithm (QLRA) wasintroduced by A. Khrennikov [20]–[28] to solve the so-called “inverseBorn’s rule problem”: to construct a representation of probabilistic databy a complex or hyperbolic probability amplitude or more general complextogether with hyperbolic which matches Born’s rule or its generalizations.The outcome from QLRA is coupled to the formula of totalprobability with an additional term corresponding to trigonometric, hyperbolicor hyper-trigonometric interference. The consistency of QLRAfor probabilistic data corresponding to trigonometric interference was recentlyproved [29].We complete the proof of the consistency of QLRA tocover hyperbolic interference as well. We will also discuss hyper trigonometricinterference. The problem of consistency of QLRA arises, becauseformally the output of QLRA depends on the order of conditioning. Fortwo observables (e.g., physical or biological) a and b, b|a- and a|b- conditionalprobabilities produce two representations, say in Hilbert spacesHb|a and Ha|b (in this paper over the hyperbolic algebra). We provethat under “natural assumptions” these two representations are unitaryequivalent (in the sense of hyperbolic Hilbert space).

1. On relations between classical and quantum theories of information and probability$(function(){PrimeFaces.cw("OverlayPanel","overlay435435",{id:"formSmash:j_idt1313:0:j_idt1322",widgetVar:"overlay435435",target:"formSmash:j_idt1313:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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