Creating and detecting specious randomness

• Published in: EPJ quantum technology Vol. 10; no. 1; p. 1
• Main Authors: Almlöf, Jonas, Vall Llosera, Gemma, Arvidsson, Elisabet, Björk, Gunnar
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-12-2023; Springer Nature B.V
• Subjects: Chi-square test; Data compression; Nanotechnology and Microengineering; Physics; Physics and Astronomy; Quantum Information Technology; Quantum Physics; Quantum random number generation; Randomness; Sequences; Spintronics; Strings; Randomness; Data compression; Randomness test
• ISSN: 2662-4400; 2196-0763
• DOI: 10.1140/epjqt/s40507-022-00158-7

We present a new test of non-randomness that tests both the lower and the upper critical limit of a
χ
2
-statistic. While checking the upper critical value has been employed by other tests, we argue that also the lower critical value should be examined for non-randomness. To this end, we prepare a binary sequence where all possible bit strings of a certain length occurs the same number of times and demonstrate that such sequences pass a well-known suite of tests for non-randomness. We show that such sequences can be compressed, and therefore are somewhat predictable and thus not fully random. The presented test can detect such non-randomness, and its novelty rests on analysing fixed-length bit string frequencies that lie closer to the
a priori
probabilities than could be expected by chance alone.