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arXiv · 2607.27015

Reliability Functions of Quantum Soft Covering and Privacy Amplification via a Mixed-Order Rényi Divergence

Shi-Bing Li·Hongsen Qiu·Xinyu Zhang
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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 $α\in[2,\infty)$. 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.

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Shi-Bing Li, Hongsen Qiu, Xinyu Zhang. 2026-08-12. Reliability Functions of Quantum Soft Covering and Privacy Amplification via a Mixed-Order Rényi Divergence. https://arxiv.org/abs/2607.27015

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