A toy model for quantum mechanics

TL;DR

This paper extends Spekkens' toy model of quantum mechanics by generalizing pure states and measurement associations, resulting in a non-signaling model that violates Bell-CHSH inequalities and naturally incorporates negative probabilities.

Contribution

The paper introduces a generalized toy model that allows Bell-CHSH violation and negative probabilities, expanding the epistemic view of quantum mechanics.

Findings

Model does not allow signaling.

Model violates Bell-CHSH inequalities.

Negative probabilities naturally arise in the model.

Abstract

The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations.