Searching for evidence of algorithmic randomness and incomputability in the output of quantum random number generators

TL;DR

This study investigates whether quantum random number generators produce sequences that are truly algorithmically random and incomputable by applying advanced tests, thereby advancing understanding of quantum randomness verification.

Contribution

The paper introduces a novel application of primality and incomputability tests to quantum RNG outputs, significantly increasing the statistical power over previous studies.

Findings

No definitive evidence of algorithmic randomness was found.

The tests successfully detected repeated patterns in highly compressible strings.

The study enhances methods for verifying quantum randomness.

Abstract

Ideal quantum random number generators (QRNGs) can produce algorithmically random and thus incomputable sequences, in contrast to pseudo-random number generators. However, the verification of the presence of algorithmic randomness and incomputability is a nontrivial task. We present the results of a search for algorithmic randomness and incomputability in the output from two different QRNGs, performed by applying tests based on the Solovay-Strassen test of primality and the Chaitin-Schwartz theorem. The first QRNG uses measurements of quantum vacuum fluctuations. The second QRNG is based on polarization measurements on entangled single photons; for this generator, we use looped (and thus highly compressible) strings that also allow us to assess the ability of the tests to detect repeated bit patterns. Compared to a previous search for algorithmic randomness, our study increases statistical power by almost 3 orders of magnitude.