Reliability Functions of Quantum Soft Covering and Privacy Amplification via a Mixed-Order R\'enyi Divergence

Abstract:In this paper, we introduce a novel mixed-order Rényi divergence and investigate its fundamental properties. Using this divergence, we define a family of mixed-order order-two Rényi mutual information and Rényi conditional entropy. We derive exact reliability functions of quantum soft covering and privacy amplification under the sandwiched Rényi divergence with order $\alpha\in[2,\infty)$. The former is jointly characterized by the sandwiched and mixed-order order-two Rényi mutual information quantities, while the latter is characterized by the corresponding conditional entropies. These results provide operational interpretations of the proposed mixed-order Rényi divergence. To the best of our knowledge, this is the first exact characterization of the reliability function for quantum soft covering.

Comments welcome!

Quantum Physics (quant-ph); Information Theory (cs.IT); Functional Analysis (math.FA)

arXiv:2607.27015 [quant-ph]

(or arXiv:2607.27015v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.27015 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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