Free randomness amplification using bipartite chain correlations

TL;DR

This paper analyzes how Bell inequality violations can be used to amplify weak randomness sources into perfect randomness, providing a detailed theoretical framework and exact asymptotic results.

Contribution

It offers a direct analysis of randomness amplification protocols using Bell inequalities, including the convex combination of no-signaling boxes and the characterization of source distributions.

Findings

Probability distributions are mixtures of permutations of Bernoulli distributions.

Partial randomness can be fully amplified using quantum correlations.

Exact asymptotic values for large measurement settings are derived.

Abstract

A direct analysis of the protocol of randomness amplification using Bell inequality violation is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. The probability distributions of bits generated by a Santha-Vazirani source are shown to be mixtures of permutations of Bernoulli distributions with parameter defined by the source. An intuitive proof is provided for the range of partial randomness from which perfect randomness can be extracted using quantum correlations violating the chain inequalities. Exact values are derived in the asymptotic limit of a large number of measurement settings.