Relational Hidden Variables and Non-Locality

Abstract

We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.

42 pages in journal style. To appear in Studia Logica

References in corpus (3)

• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• A Classification of Hidden-Variable Properties
• Quantum analogues of Hardy's nonlocality paradox

Cited by in corpus (18)

• A possibilistic no-go theorem on the Wigner's friend paradox
• Extendability in the Sheaf-theoretic Approach: Construction of Bell Models from Kochen-Specker Models
• Consequences and applications of the completeness of Hardy's nonlocality
• Fantastic Quantum Theories and Where to Find Them
• Categories of Empirical Models
• Possibilities Determine the Combinatorial Structure of Probability Polytopes
• Amalgamation and Symmetry: From Local to Global Consistency in The Finite
• A Bestiary of Sets and Relations
• Closing Bell: Boxing black box simulations in the resource theory of contextuality
• Continuous-variable nonlocality and contextuality
• On the 'Reality' of Observable Properties
• On the computational complexity of detecting possibilistic locality
• Categorical Quantum Dynamics
• On the theory of composition in physics
• Contextual Semantics: From Quantum Mechanics to Logic, Databases, Constraints, and Complexity
• Plausibility measures on test spaces
• Reflections on the PBR Theorem: Reality Criteria & Preparation Independence
• The Interplay between Quantum Contextuality and Wigner Negativity