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dc.contributor.authorVourdas, Apostolos*
dc.date.accessioned2016-10-07T14:40:21Z
dc.date.available2016-10-07T14:40:21Z
dc.date.issued2013
dc.identifier.citationVourdas A (2013) The complete Heyting algebra of subsystems and contextuality. Journal of Mathematical Physics. 54: 082105.
dc.identifier.urihttp://hdl.handle.net/10454/9747
dc.descriptionno
dc.description.abstractThe finite set of subsystems of a finite quantum system with variables in Z(n), is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more general concept than superposition. Consequently, the quantum probabilities related to commuting projectors in the subsystems, are incompatible with associativity of the join in the Heyting algebra, unless if the variables belong to the same chain. This leads to contextuality, which in the present formalism has as contexts, the chains in the Heyting algebra. Logical Bell inequalities, which contain "Heyting factors," are discussed. The formalism is also applied to the infinite set of all finite quantum systems, which is appropriately enlarged in order to become a complete Heyting algebra.
dc.relation.isreferencedbyhttp://dx.doi.org/10.1063/1.4817855
dc.subjectFinite hilbert-space; Quantum-mechanics; Hidden-variables; Inequalities; Nonlocality; Systems; Heyting algebra
dc.titleThe complete Heyting algebra of subsystems and contextuality
dc.typeJournal Article
dc.type.versionNo full-text in the repository


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