A Classification of Hidden-Variable Properties

TL;DR

This paper classifies different properties of hidden-variable models in quantum mechanics, analyzing their relationships and limitations through theorems, and clarifies which properties can coexist in models consistent with quantum phenomena.

Contribution

It introduces six properties of hidden-variable models, maps their relationships, and establishes new existence and no-go theorems to delineate feasible models.

Findings

Six properties of hidden-variable models identified and related.

Three no-go theorems (EPR, Bell, Kochen-Specker) proved to restrict properties.

Certain combinations of properties are shown to be impossible in quantum models.

Abstract

Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present six such properties and a Venn diagram of how they are related. With two existence theorems and three no-go theorems (EPR, Bell, and Kochen-Specker), we show which properties of empirically equivalent hidden-variable models are possible and which are not. Formally, our treatment relies only on classical probability models, and physical phenomena are used only to motivate which models to choose.