“…the random numbers should be unpredictable by any physical observer, that is, any observer whose actions are constrained by the laws of physics.”
A review paper in Nature by Acin and Masanes is the first paper I ever read there about random number generation! The central debate in the paper is about the notion of randomness, which the authors qualify as above. This seems to exclude the use of “our” traditional random number generators, although I do not see why they could not be used with an unpredictable initialisation, which does not have to be done according to a specific probability distribution. The only thing that matters is unpredictability.
“…the standard method for certifying randomness consists of running statistical tests1 on sequences generated by the device. However, it is unclear what passing these tests means and, in fact, it is impossible to certify with finite computational power that a given sequence is random.”
The paper supports instead physical and quantum devices. Justified or certified by [violations of] the Bell inequality, which separates classic from quantum. Not that I know anything about this. Or that I can make sense of the notations in the paper, like
which is supposed to translate that the bits are iid Uniform and independent of the environment. Actually, I understood very little of the entire review paper, which is quite frustrating since this may well be the only paper ever published in Nature about random number generation!
“…a generation rate of 42 random bits after approximately one month of measurements, was performed using two entangled ions in two traps at 1-m distance.”
It is also hard to tell whether or not this approach to quantum random number generation has foreseeable practical consequences. There already exist QRNGs, as shown by this example from ANU. And this much more readable review.