  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
selected from a Santha-Vazirani source.
