Exploring Inequality Violations by Classical Hidden Variables Numerically

TL;DR

This paper investigates the ability of classical hidden variable models to violate Bell-type inequalities through numerical simulations, comparing the robustness of CHSH and Bell inequalities in mimicking quantum correlations.

Contribution

It introduces hidden variable models that can violate Bell and CHSH inequalities with high probability, challenging assumptions about classical explanations of quantum correlations.

Findings

Hidden variables can violate Bell with 85% probability

Models can violate CHSH 50% of the time

Simulations show the importance of anti-correlation in quantum violations

Abstract

There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser-Horne-Shimony-Holt (CHSH) inequality is very robust. However, we argue that with the Einstein-Podolsky-Rosen setup, the CHSH is inferior to the Bell inequality, although and because the latter must assume anti-correlation of entangled photon singlet states. We simulate how often quantum behavior violates both inequalities, depending on the number of photons. Violating Bell 99% of the time is argued to be an ideal benchmark. We present hidden variables that violate the Bell and CHSH inequalities with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. We discuss how to present the quantum correlations to a wide audience and conclude that, when defending against claims of hidden classicality, one should demand numerical simulations and insist on anti-correlation and the full amount of Bell violation. This preprint version adds a section on realisms and shows the actual programs with output.