{
  "annotation_id": "b382c9e9-f82e-406c-af6f-c35ff6f935d3",
  "date_created": "2026-02-17T05:53:08.575000Z",
  "date_modified": "2026-02-17T05:53:08.575000Z",
  "file_hash": "b4bff7b4ba1a8a4d0fc610d41fa5c2a272eb6fcd5155c61c5c4aaabe6d5fad14",
  "private": false,
  "record": {
    "abstract": "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-R\\\u0027{e}nyi information and the Petz-Augustin information. To maximize the Petz-R\\\u0027{e}nyi information, we show that it corresponds to a convex H\\\"{o}lder-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).",
    "arxiv_id": "2601.06492",
    "authors": [
      "Chun-Neng Chu",
      "Wei-Fu Tseng",
      "Yen-Huan Li"
    ],
    "categories": [
      "cs.IT",
      "math.IT",
      "math.OC",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Algorithms for Computing the Petz-Augustin Capacity",
    "url": "https://arxiv.org/abs/2601.06492",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f02ee1f6-7d7d-4f3a-be71-395f816526be",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}