Device-independent Shannon entropy certification

TL;DR

This paper explores the certification of Shannon entropy in quantum random number generators using Bell inequalities, analyzing noise effects and providing bounds to ensure true randomness in untrusted devices.

Contribution

It introduces a method for certifying Shannon entropy in quantum RNGs, including analytical bounds and noise analysis, expanding beyond previous focus on min-entropy.

Findings

Certification of Shannon entropy is feasible with Bell inequalities.

Noise impacts the usability of Bell inequalities for entropy certification.

A tight analytical lower bound for Shannon entropy in this context is provided.

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.