Is it possible to certify that the n-bit output of a physical random number generator is “really random”? Since every fixed length sequence should be output with equal probability, there seems to be no basis on which to reject any particular output. Indeed, in the classical World it seems impossible to provide such a test.
The uniquely quantum mechanical phenomena of entanglement and Bell inequality violations allow for a remarkable random number generator. Its output is certifiably random in the following sense: if there is no information communicated between the two boxes in the randomness generating device (based, say, on the speed of light limit imposed by special relativity), and provided the output passes a simple statistical test, then the output is certifiably random. Paradoxically, the certification of randomness does not depend upon the correctness of quantum mechanics, and would even be convincing to a quantum skeptic!
The work on certifiable randomness has recently played a major role in the resolution of one of the great challenges in quantum cryptography - achieving device independence. This very strong guarantee of security allows the users of the cryptographic scheme to test in real time that its security has not been compromised.
Based on joint work with Thomas Vidick.