Generalized Rényi entropy accumulation theorem and generalized quantum probability estimation

CS/MATH Seminar - Amir Arqand, IQC

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 talk, 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 R´enyi entropies if desired, yielding fully-R´enyi 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 R´enyi entropies, and in the process we obtain some new results with respect to those frameworks as well.

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