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Quantifying the randomness of copies of noisy Popescu-Rohrlich correlations

par Bourdoncle, Boris;Pironio, Stefano ;Acín, Antonio
Référence Physical Review A, 98, 4, 042130
Publication Publié, 2018-10-01

Article révisé par les pairs

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Résumé :

In a no-signaling world, the outputs of a nonlocal box cannot be completely predetermined, a feature that is exploited in many quantum information protocols exploiting nonlocality, such as device-independent randomness generation and quantum key distribution. This relation between nonlocality and randomness can be formally quantified through the min-entropy, a measure of the unpredictability of the outputs that holds conditioned on the knowledge of any adversary that is limited only by the no-signaling principle. This quantity can easily be computed for the noisy Popescu-Rohrlich (PR) box, the paradigmatic example of nonlocality. In this paper, we consider the min-entropy associated to several copies of noisy PR boxes. In the case where n noisy PR boxes are implemented using n noncommunicating pairs of devices, it is known that each PR box behaves as an independent biased coin: the min-entropy per PR box is constant with the number of copies. We show that this does not hold in more general scenarios where several noisy PR boxes are implemented from a single pair of devices, either used sequentially n times or producing n outcome bits in a single run. In this case, the min-entropy per PR box is smaller than the min-entropy of a single PR box, and it decreases as the number of copies increases.