Unifying Hidden-Variable Problems from Quantum Mechanics by Logics of Dependence and Independence

TL;DR

This paper employs dependence and independence logics to formalize and analyze hidden-variable models in quantum mechanics, providing a unified logical framework to understand their properties and no-go theorems.

Contribution

It introduces a logical approach using team semantics to characterize hidden-variable properties and simplifies proofs of key quantum no-go theorems.

Findings

Logical formalization of hidden-variable properties

Unified proofs for probabilistic and relational models

Logical variant of Kochen-Specker theorem

Abstract

We study hidden-variable models from quantum mechanics, and their abstractions in purely probabilistic and relational frameworks, by means of logics of dependence and independence, based on team semantics. We show that common desirable properties of hidden-variable models can be defined in an elegant and concise way in dependence and independence logic. The relationship between different properties, and their simultaneous realisability can thus been formulated and a proved on a purely logical level, as problems of entailment and satisfiability of logical formulae. Connections between probabilistic and relational entailment in dependence and independence logic allow us to simplify proofs. In many cases, we can establish results on both probabilistic and relational hidden-variable models by a single proof, because one case implies the other, depending on purely syntactic criteria. We also discuss the no-go theorems by Bell and Kochen-Specker and provide a purely logical variant of the latter, introducing non-contextual choice as a team-semantical property.