Yes / The set of subsystems Sigma(m) of a finite quantum system Sigma(n) with variables in Z(n) together with logical connectives, is a Heyting algebra. The probabilities tau(m vertical bar rho(n)) Tr vertical bar B(m)rho(n)] (where B(m) is the projector to Sigma(m)) are compatible with associativity of the join in the Heyting algebra, only if the variables belong to the same chain. Consequently, contextuality in the present formalism, has the chains as contexts. Various Bell-like inequalities are discussed. They are violated, and this proves that quantum mechanics is a contextual theory.
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/10806 |
| Date | January 2014 |
| Creators | Vourdas, Apostolos |
| Source Sets | Bradford Scholars |
| Detected Language | English |
| Type | Article, Published version |
| Rights | (c) 2014 The Author. This is an Open Access article distributed under the Creative Commons CC-BY license (http://creativecommons.org/licenses/by/3.0) |
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