Possible Vulnerability of Bell-Clauser-Horne-Shimony-Holt Tests Used for Quantum Certification

A hidden variables (HVs) model is reported, which reproduces quantum predictions for Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) tests. The existence of such a model poses some limitations to quantum certifications that rely on Bell-CHSH inequality violations. The reported model does not prove wrong Bell's theorem. The latter assumes the factorability of the probability density p_AB, which rules the stochastic behavior of the HVs. The reported HVs model is based on an extended form of p_AB, which is suggested by Lebesgue's decomposition theorem for bounded functions. The considered p_AB complies with locality and realism, and also with measurement independence, parameter independence and outcome independence.