Abstract:
We construct a class of 3-dimensional photonic quantum random number
generators and prove that each generates maximally unpredictable digits via
measurements that are robust to errors. In particular, every sequence generated
is strongly incomputable; hence its quality is provable better than that
of every pseudo-random sequence. We also briefly contrast 2-dimensional
and 3-dimensional quantum random number generators, discuss photonic
implementations and show the superiority of the latter ones. These results
suggest that incomputability in physics is real and practically useful.