Regularising data for practical randomness generation

Non-local correlations that obey the no-signalling principle contain intrinsic randomness. In par- ticular, for a specific Bell experiment, one can derive relations between the amount of randomness produced, as quantified by the min-entropy of the output data, and its associated violation of a Bell inequality. In practice, due to finite sampling, certifying randomness requires the development of statistical tools to lower-bound the min-entropy of the data as a function of the estimated Bell viola- tion. The quality of such bounds relies on the choice of the certificate, i.e., the Bell inequality whose violation is estimated. In this work, we propose a method for choosing efficiently such a certificate. It requires sacrificing a part of the output data in order to estimate the underlying correlations. Regularizing this estimate then allows one to solve the related guessing probability problem, whose dual formulation provides a Bell inequality suitable for certifying practical randomness. In order to show the efficiency of our method, we carry out several numerical simulations of a Bell experiment: we nearly always obtain higher min-entropy rates than when we use a pre-established Bell inequality, namely the Clauser-Horne-Shimony-Holt inequality.