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Regularising data for practical randomness generation
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DOI：10.1088/2058-9565/ab01e8.png)
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Assuming that the no-signalling principle holds, non-local correlations contain intrinsic randomness. In particular, for a specificBell experiment, one can derive relations between the amount of randomness produced, as quantified by themin-entropy of the output data, and its associated violation of a Bell inequality. In practice, due tofinite sampling, certifying randomness requires the development of statistical tools to lower-bound themin-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.
Keyword:
Randomness generation
Bell nonlocality
device-independent information processing
quantum information theory
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