Tsirelson Polytopes and Randomness Generation*

We classify the extreme points of polytopes of probability distributions in the (2,2,2) Bell-CHSH setting that are induced by a single Tsirelson bound. We also do the same for a parametrized family of polytopes obtained from two Tsirelson bounds that interact non-trivially. Such constructions can be applied to device-independent random number generation using the method of probability estimation factors (PRA 98:040304(R) (2018), arXiv:1812.07786, arXiv:1806.04553). We demonstrate a meaningful improvement in certified randomness applying the new polytopes characterized here.