Are there fundamentally random processes in nature? Theoretical predictions,
confirmed experimentally, such as the violation of Bell inequalities, point to
an affirmative answer. However, these results are based on the assumption that
measurement settings can be chosen freely at random, so assume the existence of
perfectly free random processes from the outset. Here we consider a scenario in
which this assumption is weakened and show that partially free random bits can
be amplified to make arbitrarily free ones. More precisely, given a source of
random bits whose correlation with other variables is below a certain
threshold, we propose a procedure for generating fresh random bits that are
virtually uncorrelated with all other variables. We also conjecture that such
procedures exist for any non-trivial threshold. Our result is based solely on
the no-signalling principle, which is necessary for the existence of free
randomness.Comment: 5+7 pages, 2 figures. Updated to match published versio
