Generalized Rényi entropy accumulation theorem and generalized quantum probability estimation

Abstract

The entropy accumulation theorem, and its subsequent generalized version, is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size bounds it yields are not necessarily optimal, and furthermore it relies on the construction of an affine min-tradeoff function, which can often be challenging to construct optimally in practice. In this work, we address both of these challenges simultaneously by deriving a new entropy accumulation bound. Our bound yields significantly better finite-size performance, and can be computed as an intuitively interpretable convex optimization, without any specification of affine min-tradeoff functions. Furthermore, it can be applied directly at the level of Rényi entropies if desired, yielding fully-Rényi security proofs. Our proof techniques are based on elaborating on a connection between entropy accumulation and the frameworks of quantum probability estimation or $f$-weighted Rényi entropies, and in the process we obtain some new results with respect to those frameworks as well. In particular, those findings imply that our bounds apply to prepare-and-measure protocols without the virtual tomography procedures or repetition-rate restrictions previously required for entropy accumulation.

Close to published version, with more explanations below Theorem 4.1. Changelog: significant restructuring; some lemmas renumbered/added; statements improved/simplified; removed parts superceded by arXiv:2502.01611 & arXiv:2502.02563; renamed QES-entropies to align with prior work; addressed error regarding rate-bounding channels in [v3]-[v4] by defining a "convex range"; fixed Sec. 5.2.1 typos