The extension problem for partial Boolean structures in Quantum Mechanics

Abstract

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.

A number of misprints have been corrected and some terminology changed in order to avoid possible ambiguities

References in corpus (2)

• Experimentally testable state-independent quantum contextuality
• Universality of state-independent violation of correlation inequalities for noncontextual theories

Cited by in corpus (9)

• Kochen-Specker Contextuality
• All noncontextuality inequalities for the n-cycle scenario
• Entropic Test of Quantum Contextuality
• Necessary and sufficient condition for contextuality from incompatibility
• Bell inequalities from variable elimination methods
• Indistinguishability of causal relations from limited marginals
• The Exclusivity Principle and the Set of Quantum Correlations
• Bell inequalities as constraints on unmeasurable correlations
• On random classical marginal problems with applications to quantum information theory