Abstract
A direct analysis of the task of randomness amplification from Santha-Vazirani sources using the violation of the chained Bell inequality is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. This analysis is used to find the exact threshold value of the initial randomness parameter from which perfect randomness can be extracted in the asymptotic limit of a large number of measurement settings. As a byproduct, we provide a tool for the analysis of randomness amplification protocols, namely a general characterization of the probability distributions of bits generated by Santha-Vazirani sources, which are shown to be mixtures of specific permutations of Bernoulli distributions with a parameter defined by the source.
- Received 14 February 2014
- Revised 26 August 2014
DOI:https://doi.org/10.1103/PhysRevA.90.032322
©2014 American Physical Society