Pearle's Hidden-Variable Model Revisited

TL;DR

This paper revisits Pearle's 1970 local hidden variables model that reproduces quantum correlations through data rejection, correcting a normalization mistake, simplifying the model, and providing visualizations and simulations.

Contribution

It corrects a normalization error in Pearle's original formulas and demonstrates that the model is simpler than previously thought, with visualizations and simulations included.

Findings

Corrected Pearle's formulas for the hidden-variable model.

Showed the model's simplicity through visualizations.

Provided simulation code demonstrating the model.

Abstract

Pearle (1970) gave an example of a local hidden variables model which exactly reproduced the singlet correlations of quantum theory, through the device of data-rejection: particles can fail to be detected in a way which depends on the hidden variables carried by the particles and on the measurement settings. If the experimenter computes correlations between measurement outcomes of particle pairs for which both particles are detected, he is actually looking at a subsample of particle pairs, determined by interaction involving both measurement settings and the hidden variables carried in the particles. We correct a mistake in Pearle's formulas (a normalization error) and more importantly show that the model is more simple than first appears. We illustrate with visualisations of the model and with a small simulation experiment, with code in the statistical programming language R included in the paper. Open problems are discussed.