Randomness comes in two qualitatively different forms. Apparent randomness can result both from ignorance or lack of control of degrees of freedom in the system. In contrast, intrinsic randomness should not be ascribable to any such cause. While classical systems only possess the first kind of randomness, quantum systems are believed to exhibit some intrinsic randomness. In general, any observed random process includes both forms of randomness. In this work, we provide quantum processes in which all the observed randomness is fully intrinsic. These results are derived under minimal assumptions: the validity of the no-signalling principle and an arbitrary (but not absolute) lack of freedom of choice. The observed randomness tends to a perfect random bit when increasing the number of parties, thus defining an explicit process attaining full randomness amplification.
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