Abstract:
Our aim is to experimentally study the possibility of distinguishing between quantum
sources of randomness—recently proved to be theoretically incomputable—and some
well-known computable sources of pseudo-randomness. Incomputability is a necessary,
but not sufficient “symptom” of “true randomness.” We base our experimental approach
on algorithmic information theory which provides characterizations of algorithmic random
sequences in terms of the degrees of incompressibility of their finite prefixes. Algorithmic
random sequences are incomputable, but the converse implication is false. We
have performed tests of randomness on pseudo-random strings (finite sequences) of length
232 generated with software (Mathematica, Maple), which are cyclic (so, strongly computable),
the bits of p, which is computable, but not cyclic, and strings produced by quantum
measurements (with the commercial device Quantis and by the Vienna IQOQI group).
Our empirical tests indicate quantitative differences, some statistically significant, between
computable and incomputable sources of “randomness.”