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arXiv · 1802.04703

Regularising data for practical randomness generation

Boris Bourdoncle·Pei-Sheng Lin·Denis Rosset·Antonio Acín·Yeong-Cherng Liang
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Abstract

Non-local correlations that obey the no-signalling principle 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. It 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.

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Boris Bourdoncle, Pei-Sheng Lin, Denis Rosset, Antonio Acín, Yeong-Cherng Liang. 2018-02-13. Regularising data for practical randomness generation. https://doi.org/10.1088/2058-9565%2Fab01e8

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