Extensive search of Shannon entropy-based randomness certification protocols

TL;DR

This paper conducts an extensive analysis of Shannon entropy-based Bell inequalities to enhance randomness certification in quantum systems, identifying key expressions and extending self-testing methods for better quantum correlation characterization.

Contribution

It provides a large-scale quantitative analysis of Bell expressions for randomness certification and introduces an extension incorporating self-testing concepts for improved quantum correlation assessment.

Findings

Identified five Bell expressions with high entropy scores under noise.

Analyzed over half a million Bell expressions for randomness certification.

Extended self-testing framework for comprehensive quantum correlation evaluation.

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 $Boxes(\alpha, B)$ and the corresponding measure $Flex(\alpha, B)$.