@article{Bourdoncle_2019,
doi = {10.1088/2058-9565/ab01e8},
url = {https://doi.org/10.1088%2F2058-9565%2Fab01e8},
year = 2019,
month = {feb},
publisher = {{IOP} Publishing},
volume = {4},
number = {2},
pages = {025007},
author = {Boris Bourdoncle and Pei-Sheng Lin and Denis Rosset and Antonio Ac{\'{\i}}n and Yeong-Cherng Liang},
title = {Regularising data for practical randomness generation},
journal = {Quantum Science and Technology},
annote = {Assuming that the no-signalling principle holds, non-local correlations contain intrinsic randomness. In particular, 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 violation. The quality of such bounds relies on the choice of certificate, i.e. the Bell inequality whose violation is estimated. In this work, we propose a method for choosing efficiently such a certificate and analyse, by means of extensive numerical simulations (with various choices of parameters), the extent to which it works. The method requires sacrificing a part of the output data in order to estimate the underlying correlations. Regularising this estimate then allows one to find a Bell inequality that is well suited for certifying practical randomness from these specific correlations. We then study the effects of various parameters on the obtained min-entropy bound and explain how to tune them in a favourable way. Lastly, we carry out several numerical simulations of a Bell experiment to show the efficiency of our method: we nearly always obtain higher min-entropy rates than when we use a pre-established Bell inequality, namely the Clauser–Horne–Shimony–Holt inequality.}
}