Contextuality and Random Variables

TL;DR

This paper explores the concept of contextuality in systems of random variables, focusing on how variables change with context and how this relates to their joint distributions and couplings.

Contribution

It introduces a formal framework for understanding contextuality through maximal couplings and characterizes noncontextual systems based on these couplings.

Findings

Contextuality is characterized by the replacement of variables across contexts.

Noncontextual systems have a coupling with maximal marginals.

The framework clarifies how context affects the identity of random variables.

Abstract

Abstract Contextuality is a property of systems of random variables. The identity of a random variable in a system is determined by its joint distribution with all other random variables in the same context. When context changes, a variable measuring some property is instantly replaced by another random variable measuring the same property, or instantly disappears if this property is not measured in the new context. This replacement/disappearance requires no action, signaling, or disturbance, although it does not exclude them. The difference between two random variables measuring the same property in different contexts is measured by their maximal coupling, and the system is noncontextual if one of its overall couplings has these maximal couplings as its marginals.