Isaac Newton Institute for Mathematical Sciences

Robust Device-Independent Randomness Amplification

Presenter: Ravishankar Ramanathan (University of Gdansk, National Quantum Information Centre of Gdansk, Poland)

Co-authors: Fernando G. S. L. Brandao (University College London), Andrzej Grudka (Adam Mickiewicz University, Poznan, Poland), Karol Horodecki (University of Gdansk, National Quantum Information Centre of Gdansk, Poland), Michal Horodecki (University of Gdansk, National Quantum Information Centre of Gdansk, Poland), Pawel Horodecki (Technical University of Gdansk, National Quantum Information Centre of Gdansk, Poland)

Abstract

In randomness amplification a slightly random source is used to produce an improved random source. Perhaps surprisingly, a single source of randomness cannot be amplified at all classically. However, the situation is different if one considers correlations allowed by quantum mechanics as an extra resource. Here we present a protocol that amplifies Santha-Vazirani sources arbitrarily close to deterministic into fully random sources. The protocol is device independent, depending only on the observed statistics of the devices and on the validity of the no-signaling principle between different devices. It improves previously-known protocols in two respects. First the protocol is tolerant to noise so that even noisy quantum-mechanical systems give rise to good devices for the protocol. Second it is simpler, being based on the violation of a four-party Bell inequality and on the XOR as a hash function. As a technical tool we prove a new de Finetti theorem where the subsystems are s elected from a Santha-Vazirani source.