Event-Based and LHV Simulation of an EPR-B Experiment: EPR-Simple and EPR-Clocked

In this note, I analyze the code and the data generated by M. Fodje's (2013) simulation programs "epr-simple" and "epr-clocked". They were written in Python published on Github only, initially without any documentation at all of how they worked. Inspection of the code 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 signaling. The coincidence-loophole model is actually a clever modification of the detection-loophole model. Because of this, however, it cannot lead to optimal efficiency. Later versions of the programs included an explanation of how they worked, including formulas, though still no reference whatever to the literature on the two loopholes which Fodje exploits, not even to the concept of an experimental (i.e., in principle, avoidable) loophole. The documentation available now does make a lot of the "reverse engineering" in this paper superfluous. I plan to incorporate its results in a new paper with a wider focus.