Extensive search of Shannon entropy-based randomness certification protocols

Quantum technologies offer significant advancements in information processing and communication, notably in the domain of random number generation (RNG). The use of Bell inequalities enables users to certify the randomness of outputs produced by untrusted quantum RNG devices. We present a method for quantitatively analyzing Bell expressions used to certify randomness in quantum systems. Using this method, we conducted a comprehensive analysis on more than half a million Bell expressions involving configurations with four measurement settings for one party and three for the other. We identified five notable examples based on entropy scores under varying levels of white noise. As an extension of these results, we further incorporate the concept of self-testing for boxes (Banacki et al 2022, New J. Phys. 24 083003), enabling a more comprehensive characterization of quantum correlations through the evaluation of Boxes(α, B) and the corresponding measure Flex(α, B).