Generalized Rényi entropy accumulation theorem and generalized quantum probability estimation

• URL: http://arxiv.org/abs/2405.05912v4
• Date: Sat, 26 Oct 2024 20:28:15 GMT
• Title: Generalized Rényi entropy accumulation theorem and generalized quantum probability estimation
• Authors: Amir Arqand, Thomas A. Hahn, Ernest Y. -Z. Tan,
• Abstract summary: entropy accumulation theorem is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. It relies on the construction of an affine min-tradeoff function, which can often be challenging to construct optimally in practice. We deriving a new entropy accumulation bound, which yields significantly better finite-size performance.
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• 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 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. 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.

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