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arXiv:2511.22771

Extensive search of Shannon entropy-based randomness certification protocols

Robert Okuła, Piotr Mironowicz

quant-phSubmitted Nov 27, 2025• Announced Dec 1, 2025• 0 citations• Revised Sep 20, 2026 (v2)
v1 · Nov 27, 2025v2 · Sep 20, 2026
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Abstract

Quantum technologies offer significant advancements in information processing and communication, notably in the domain of random number generation (RNG). The use of Bell inequalities enables users to certify the randomness of outputs produced by untrusted quantum RNG devices. We present a method for quantitatively analyzing Bell expressions used to certify randomness in quantum systems. Using this method, we conducted a comprehensive analysis on more than half a million Bell expressions involving configurations with four measurement settings for one party and three for the other. We identified five notable examples based on entropy scores under varying levels of white noise. As an extension of these results, we further incorporate the concept of self-testing for boxes (Banacki et al 2022, New J. Phys. 24 083003), enabling a more comprehensive characterization of quantum correlations through the evaluation of $Boxes(α, B)$ and the corresponding measure $Flex(α, B)$.

Comments
14 pages, 5 figures, 5 tables

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Abstract Quantum technologies promise information processing and communication technology advancements, including random number generation (RNG). Using Bell inequalities, a user of a quantum RNG hardware can certify that the values provided by an untrusted device are truly random. This problem has been extensively studied for von Neumann and min-entropy as a measure of randomness. However, in this paper, we analyze the feasibility of such verification for Shannon entropy. We investigate how the usability of various Bell inequalities differs depending on the presence of noise. Moreover, we present the benefit of certification for Shannon compared to min-entropy, as well as the tight analytical lower bound for Shannon entropy in randomness certification.
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