  We demonstrate that amplification of arbitrarily weak randomness is possible
using quantum resources. We present a randomness amplification protocol that
involves Bell experiments. We find a Bell inequality which can amplify
arbitrarily weak randomness and give a detailed analysis of the protocol
involving it. Our analysis includes finding a sufficient violation of Bell
inequality as a function of the initial quality of randomness. It has a very
important property that for any quality the required violation is strictly
lower than possible to obtain using quantum resources. Among other things, it
means that the protocol takes a finite amount of time to amplify arbitrarily
weak randomness.
