pdf files of
Programme Booklet >>
and
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Sponsors

Pauli Center for Theoretical Studies

The Swiss National Science Foundation

ETH Zurich (Computer Science and Physics Department)

Quantum Science and Technology

CQT Singapore

QAP European Project

Sandia National Laboratories

Institute for Quantum Computing

id Quantique

Random numbers certified by Bell’s theorem

Stefano Pironio, University of Geneva

joint work with Antonio Acin, Antoine Boyer de la Giroday, and Serge Massar

Randomness is difficult to characterize mathematically, and its generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect.
Here, we show that the non-local correlations of entangled quantum particles can be used to produce private randomness without the need for any assumptions on the internal working of the devices used in the generation. This strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation.
More spefically, we show that untrusted devices that violate a Bell inequality can be used as "randomness expanders", where a small private random seed of size O(√n log√n) is expanded into a longer private random string. Although the final output string may not be uniformly random, our analisis guarantees that it contains at least O(n) bits of entropy. With the help of a small initial private random seed, the output string can then be classically processed using a randomness extractor to convert it into a string of size O(n) that is nearly uniform and uncorrelated to the information of an adversary.