Algorithms for Computing the Petz-Augustin Capacity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908756968734720 |
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| author | Chu, Chun-Neng Tseng, Wei-Fu Li, Yen-Huan |
| author_facet | Chu, Chun-Neng Tseng, Wei-Fu Li, Yen-Huan |
| contents | We propose the first algorithms with non-asymptotic convergence guarantees for computing the Petz-Augustin capacity, which generalizes the channel capacity and characterizes the optimal error exponent in classical-quantum channel coding. This capacity can be equivalently expressed as the maximization of two generalizations of mutual information: the Petz-Rényi information and the Petz-Augustin information. To maximize the Petz-Rényi information, we show that it corresponds to a convex Hölder-smooth optimization problem, and hence the universal fast gradient method of Nesterov (2015), along with its convergence guarantees, readily applies. Regarding the maximization of the Petz-Augustin information, we adopt a two-layered approach: we show that the objective function is smooth relative to the negative Shannon entropy and can be efficiently optimized by entropic mirror descent; each iteration of entropic mirror descent requires computing the Petz-Augustin information, for which we propose a novel fixed-point algorithm and establish its contractivity with respect to the Thompson metric. Notably, this two-layered approach can be viewed as a generalization of the mirror-descent interpretation of the Blahut-Arimoto algorithm due to He et al. (2024). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_06492 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algorithms for Computing the Petz-Augustin Capacity Chu, Chun-Neng Tseng, Wei-Fu Li, Yen-Huan Information Theory Optimization and Control Quantum Physics We propose the first algorithms with non-asymptotic convergence guarantees for computing the Petz-Augustin capacity, which generalizes the channel capacity and characterizes the optimal error exponent in classical-quantum channel coding. This capacity can be equivalently expressed as the maximization of two generalizations of mutual information: the Petz-Rényi information and the Petz-Augustin information. To maximize the Petz-Rényi information, we show that it corresponds to a convex Hölder-smooth optimization problem, and hence the universal fast gradient method of Nesterov (2015), along with its convergence guarantees, readily applies. Regarding the maximization of the Petz-Augustin information, we adopt a two-layered approach: we show that the objective function is smooth relative to the negative Shannon entropy and can be efficiently optimized by entropic mirror descent; each iteration of entropic mirror descent requires computing the Petz-Augustin information, for which we propose a novel fixed-point algorithm and establish its contractivity with respect to the Thompson metric. Notably, this two-layered approach can be viewed as a generalization of the mirror-descent interpretation of the Blahut-Arimoto algorithm due to He et al. (2024). |
| title | Algorithms for Computing the Petz-Augustin Capacity |
| topic | Information Theory Optimization and Control Quantum Physics |
| url | https://arxiv.org/abs/2601.06492 |