Faithful orthogonal representations of graphs from partition logics

Abstract

The graphs induced by partition logics allow a dual probabilistic interpretation: a classical one for which probabilities lie on the convex hull of the dispersion-free weights, and another one, suggested independently from the quantum Born rule, in which probabilities are formed by the (absolute) square of the inner product of state vectors with the faithful orthogonal representations of the respective graph. Two immediate consequences are the demonstration that the logico-empirical structure of observables does not determine the type of probabilities alone, and that complementarity does not imply contextuality.

6 pages, 2 figures

References in corpus (9)

• A simple test for hidden variables in spin-1 system
• Simple explanation of the quantum violation of a fundamental inequality
• (Non-)Contextuality of Physical Theories as an Axiom
• Logical equivalence between generalized urn models and finite automata
• Staging quantum cryptography with chocolate balls
• Specker's fundamental principle of quantum mechanics
• Orthogonal Representation of Graphs
• Quantum contextuality from a simple principle?
• Contextuality in Quantum Mechanics: Testing the Klyachko Inequality

Cited by in corpus (7)

• Extensions of Hardy-type true-implies-false gadgets to classically obtain indistinguishability
• Generalized Greenberger-Horne-Zeilinger arguments from quantum logical analysis
• Extending Kolmogorov's axioms for a generalized probability theory on collections of contexts
• Varieties of contextuality based on probability and structural nonembeddability
• Propositional counter-factual definiteness and the EPR paradox
• Quantum violation of the Suppes-Zanotti inequalities and "contextuality"
• Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables