Event based simulation of an EPR-B experiment by local hidden variables: epr-simple and epr-clocked

TL;DR

This paper analyzes Python-based simulations of EPR-B experiments using local hidden variables, evaluating their loophole models with modified Bell inequalities and discussing their efficiencies and signaling issues.

Contribution

It provides a detailed evaluation of Fodje's simulation programs using adjusted Bell inequalities, revealing their similarities to Pearle's model and their efficiency limitations.

Findings

Detection-loophole model closely resembles Pearle's 1970 model.

Observed efficiencies are approximately 81% and 55%.

Models exhibit signaling in joint detection rates.

Abstract

In this note, I analyze the data generated by M. Fodje's (2013, 2014) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions showed that they made use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signalling. His coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.