2009/12/22 by Cristian S. Calude, Calude, Cristian S., Michael J. Dinneen +5
Computer Science · Mathematics · Physics and Astronomy · #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.0912.4379
openalex publication_date 2009/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 π, 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".