On a sigmoid-based model for quantum correlations in the EPR paradox

A theoretical and numerical analysis of a Bell-type experiment is presented, where measurements are modeled using a threshold mechanism based on a sigmoid function that exploits the detection loophole and violates the fair sampling assumption. The experimental setup measures correlations between linear polarization of entangled photons, prepared in non-maximally entangled states. The numerical simulation shows the model's limitations with respect to quantum mechanical theoretical predictions, demonstrates that this mechanism leads to violation of Bell's inequality, and could provide insights into the nature of spooky measurements at a distance.