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arXiv · 2601.10558

A Mirror-Descent Algorithm for Computing the Petz-R\'enyi Capacity of Classical-Quantum Channels

Yu-Hong Lai·Hao-Chung Cheng
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Abstract

We study the computation of the $\alpha$-R\'enyi capacity of a classical-quantum (c-q) channel for $\alpha\in(0,1)$. We propose an exponentiated-gradient (mirror descent) iteration that generalizes the Blahut-Arimoto algorithm. Our analysis establishes relative smoothness with respect to the entropy geometry, guaranteeing a global sublinear convergence of the objective values. Furthermore, under a natural tangent-space nondegeneracy condition (and a mild spectral lower bound in one regime), we prove local linear (geometric) convergence in Kullback-Leibler divergence on a truncated probability simplex, with an explicit contraction factor once the local curvature constants are bounded.

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Yu-Hong Lai, Hao-Chung Cheng. 2026-01-15. A Mirror-Descent Algorithm for Computing the Petz-R\'enyi Capacity of Classical-Quantum Channels. https://arxiv.org/abs/2601.10558

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