A Mirror-Descent Algorithm for Computing the Petz-Rényi Capacity of Classical-Quantum Channels

• URL: http://arxiv.org/abs/2601.10558v1
• Date: Thu, 15 Jan 2026 16:22:52 GMT
• Title: A Mirror-Descent Algorithm for Computing the Petz-Rényi Capacity of Classical-Quantum Channels
• Authors: Yu-Hong Lai, Hao-Chung Cheng,
• Abstract summary: We study the computation of the capacity of a classical-quantum (c-q) channel for $in(0,1)$.<n>We propose an exponentiated-gradient (mirror descent) that generalizes the Blahut-Arimoto algorithm.
• Score: 13.098901971644656
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the computation of the $α$-Rényi capacity of a classical-quantum (c-q) channel for $α\in(0,1)$. 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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