  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.
