Experimental violations of Bell inequalities are in general vulnerable to so-called "loopholes." In this work, we analyse the characteristics of a loophole-free Bell test with photons, closing simultaneously the locality, freedom-of-choice, fair-sampling (i.e. detection), coincidence-time, and memory loopholes. We pay special attention to the effect of excess predictability in the setting choices due to non-ideal random number generators. We discuss necessary adaptations of the CH/Eberhard inequality when using such imperfect devices and -- using Hoeffding's inequality and Doob's optional stopping theorem -- the statistical analysis in such Bell tests.
@article{arxiv.1411.4787,
title = {Requirements for a loophole-free photonic Bell test using imperfect setting generators},
author = {Johannes Kofler and Marissa Giustina and Jan-Åke Larsson and Morgan W. Mitchell},
journal= {arXiv preprint arXiv:1411.4787},
year = {2016}
}