Exploring inequality violations by classical hidden variables numerically

• The widely assumed superiority of the CHSH fails in the EPR problem.
• We simulate Bell type inequalities behavior depending on the number of photons.
• The core of Bell’s theorem in the EPR setup is introduced in a simple way understandable to a wide audience.
• We present hidden variables that violate both inequalities with 50% probability.
• Algorithms have been supplied in form of Mathematica programs.

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.