A Mirror-Descent Algorithm for Computing the Petz-Rényi Capacity of Classical-Quantum Channels
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912826457587712 |
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| author | Lai, Yu-Hong Cheng, Hao-Chung |
| author_facet | Lai, Yu-Hong Cheng, Hao-Chung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10558 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Mirror-Descent Algorithm for Computing the Petz-Rényi Capacity of Classical-Quantum Channels Lai, Yu-Hong Cheng, Hao-Chung Quantum Physics Information Theory Optimization and Control 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. |
| title | A Mirror-Descent Algorithm for Computing the Petz-Rényi Capacity of Classical-Quantum Channels |
| topic | Quantum Physics Information Theory Optimization and Control |
| url | https://arxiv.org/abs/2601.10558 |