Analytic R\'enyi Entropy Bounds for Device-Independent Cryptography

TL;DR

This paper introduces a straightforward analytical approach to derive tighter finite-size security bounds for device-independent cryptography protocols based on the CHSH game, enhancing the reliability of quantum cryptographic implementations.

Contribution

It provides a simple method to analytically solve key-rate optimization problems using Rènyi entropies, leading to improved finite-size security proofs for CHSH-based protocols.

Findings

Tighter finite-size security bounds achieved

Analytical solutions for key-rate optimization provided

Enhanced security proofs for device-independent cryptography

Abstract

Device-independent (DI) cryptography represents the highest level of security, enabling cryptographic primitives to be executed safely on uncharacterized devices. Moreover, with successful proof-of-concept demonstrations in randomness expansion, randomness amplification, and quantum key distribution, the field is steadily advancing toward commercial viability. Critical to this continued progression is the development of tighter finite-size security proofs. In this work, we provide a simple method to obtain tighter finite-size security proofs for protocols based on the CHSH game, which is the nonlocality test used in all of the proof-of-concept experiments. We achieve this by analytically solving key-rate optimization problems based on R\'enyi entropies, providing a simple method to obtain tighter finite-size key rates.