The extension problem for partial Boolean structures in Quantum Mechanics

Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presen...

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Bibliographic Details
Published in:arXiv.org 2011-01
Main Authors: Budroni, Costantino, Morchio, Giovanni
Format: Article
Language:English
Subjects:
Bell's inequality
Boolean algebra
Economic models
Quantum mechanics
Online Access:Get full text
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Summary:Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presented, allowing for a discussion of partial classical extension, amounting to reduction of the number of contexts, classical representability arising as a special case. As a result, known techniques are generalized and some of the associated computational difficulties overcome. The implications on the discussion of Boole-Bell inequalities are indicated.
ISSN:2331-8422
DOI:10.48550/arxiv.1010.4662