How Random Is Quantum Randomness? An Experimental Approach

TL;DR

This paper experimentally investigates whether quantum sources of randomness can be distinguished from pseudo-random sources using algorithmic information theory, revealing statistically significant differences in their incompressibility.

Contribution

It introduces an experimental approach to differentiate quantum randomness from pseudo-randomness based on incompressibility tests, bridging theory and empirical analysis.

Findings

Quantum randomness shows higher incompressibility than pseudo-random sequences.

Statistically significant differences found between quantum and computable sources.

Empirical tests support the theoretical distinction between true and pseudo-randomness.

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 $2^{32}$ generated with software (Mathematica, Maple), which are cyclic (so, strongly computable), the bits of $\pi$, 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".