Finite-Size Analysis of Prepare-and-Measure and Decoy-State Quantum Key Distribution via Entropy Accumulation

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-trade-off 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-trade-off function. Our approach also addresses some numerical-stability challenges specific to prepare-and-measure protocols, which have not been addressed in previous works.