Finite-size analysis of prepare-and-measure and decoy-state QKD via entropy accumulation

TL;DR

This paper advances finite-size security analysis of prepare-and-measure quantum key distribution protocols, especially decoy-state protocols, by improving entropy bounds, optimizing tradeoff functions, and addressing numerical stability issues using the generalized entropy accumulation theorem.

Contribution

It introduces new techniques for applying the GEAT to generic prepare-and-measure QKD protocols, with tighter entropy bounds and improved numerical stability.

Findings

Tighter entropy bounds for decoy-state protocols.

Enhanced methods for optimizing min-tradeoff functions.

Addressed numerical stability issues in finite-size analysis.

Abstract

An important goal in quantum key distribution (QKD) is the task of providing a finite-size security proof without the assumption of collective attacks. For prepare-and-measure QKD, one approach for obtaining such proofs is the generalized entropy accumulation theorem (GEAT), but thus far it has only been applied to study a small selection of protocols. In this work, we present techniques for applying the GEAT in finite-size analysis of generic prepare-and-measure protocols, with a focus on decoy-state protocols. In particular, we present an improved approach for computing entropy bounds for decoy-state protocols, which has the dual benefits of providing tighter bounds than previous approaches (even asymptotically) and being compatible with methods for computing min-tradeoff functions in the GEAT. Furthermore, we develop methods to incorporate some improvements to the finite-size terms in the GEAT, and implement techniques to automatically optimize the min-tradeoff function. Our approach also addresses some numerical stability challenges specific to prepare-and-measure protocols, which were not addressed in previous works.