• Open Access

Security and composability of randomness expansion from Bell inequalities

Serge Fehr, Ran Gelles, and Christian Schaffner
Phys. Rev. A 87, 012335 – Published 30 January 2013

Abstract

The nonlocal behavior of quantum mechanics can be used to generate guaranteed fresh randomness from an untrusted device that consists of two nonsignalling components; since the generation process requires some initial fresh randomness to act as a catalyst, one also speaks of randomness expansion. R. Colbeck and A. Kent [J. Phys. A 44, 095305 (2011)] proposed the first method for generating randomness from untrusted devices, but without providing a rigorous analysis. This was addressed subsequently by S. Pironio et al. [Nature (London) 464, 1021 (2010)], who aimed at deriving a lower bound on the min-entropy of the data extracted from an untrusted device based only on the observed nonlocal behavior of the device. Although that article succeeded in developing important tools for reaching the stated goal, the proof itself contained a bug, and the given formal claim on the guaranteed amount of min-entropy needs to be revisited. In this paper we build on the tools provided by Pironio et al. and obtain a meaningful lower bound on the min-entropy of the data produced by an untrusted device based on the observed nonlocal behavior of the device. Our main result confirms the essence of the (improperly formulated) claims of Pironio et al. and puts them on solid ground. We also address the question of composability and show that different untrusted devices can be composed in an alternating manner under the assumption that they are not entangled. This enables superpolynomial randomness expansion based on two untrusted yet unentangled devices.

  • Figure
  • Received 20 September 2012

DOI:https://doi.org/10.1103/PhysRevA.87.012335

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Serge Fehr1, Ran Gelles2, and Christian Schaffner1,3

  • 1Centrum Wiskunde & Informatica, Amsterdam, Netherlands
  • 2Department of Computer Science, University of California, Los Angeles, California 90095, USA
  • 3Institute for Logic, Language and Computation (ILLC), University of Amsterdam, Amsterdam, Netherlands

See Also

Security of practical private randomness generation

Stefano Pironio and Serge Massar
Phys. Rev. A 87, 012336 (2013)

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 87, Iss. 1 — January 2013

Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×