Free randomness amplification using bipartite chain correlations

Andrzej Grudka, Karol Horodecki, Michał Horodecki, Paweł Horodecki, Marcin Pawłowski, and Ravishankar Ramanathan
Phys. Rev. A 90, 032322 – Published 22 September 2014

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

Authors & Affiliations

Andrzej Grudka1, Karol Horodecki2,3, Michał Horodecki2,4, Paweł Horodecki2,5, Marcin Pawłowski4,6, and Ravishankar Ramanathan2,4

  • 1Faculty of Physics, Adam Mickiewicz University, 61-614, Poznań, Poland
  • 2National Quantum Information Center of Gdańsk, 81-824, Sopot, Poland
  • 3Institute of Informatics, University of Gdańsk, 80-952, Gdańsk, Poland
  • 4Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952, Gdańsk, Poland
  • 5Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-233, Gdańsk, Poland
  • 6Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK

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Issue

Vol. 90, Iss. 3 — September 2014

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