Negative Probabilities and Contextuality

TL;DR

This paper explores the use of negative probabilities as a theoretical framework for understanding contextuality in physics and psychology, aligning with the contextuality-by-default approach and illustrating with simple examples.

Contribution

It provides a tutorial on negative probabilities, integrating it with the contextuality-by-default framework and demonstrating its application through examples in physics and psychology.

Findings

Negative probabilities can model contextuality in various systems.

The approach aligns with existing contextuality frameworks.

Examples illustrate the applicability across disciplines.

Abstract

There has been a growing interest, both in physics and psychology, in understanding contextuality in experimentally observed quantities. Different approaches have been proposed to deal with contextual systems, and a promising one is contextuality-by-default, put forth by Dzhafarov and Kujala. The goal of this paper is to present a tutorial on a different approach: negative probabilities. We do so by presenting the overall theory of negative probabilities in a way that is consistent with contextuality-by-default and by examining with this theory some simple examples where contextuality appears, both in physics and psychology.