{
  "abstract": "Computing the optimal success probability for transmitting classical messages through a single use of a quantum channel is NP-hard, even for two messages. An existing semidefinite programming hierarchy based on symmetric extensions provides convergent upper bounds with an a priori error estimate that decays as the inverse square root of the extension level. In this work, we construct a Hermitian sum-of-squares hierarchy for an arbitrary number of messages and prove quadratic convergence in its level. The error bound is proportional to the advantage over random guessing. Our approach combines state-discrimination duality with positive polynomial kernels on products of spheres to construct feasible polynomial dual certificates. For binary messages, the resulting bounds give a multiplicative approximation from above of the trace-norm contraction coefficient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09629",
  "author_total": 2,
  "authors": [
    {
      "name": "Hoang Ta"
    },
    {
      "name": "Hoang Anh Tran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18r82hcfyff4y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09629",
  "fulltext_url": null,
  "id": "18r82hcfyff4y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09629",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7212175414",
  "pdf_url": "https://arxiv.org/pdf/2609.09629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18r82hcfyff4y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.09629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09629"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Sum-of-Squares Hierarchy with Quadratic Convergence for Quantum Channel Coding",
  "title_text": "A Sum-of-Squares Hierarchy with Quadratic Convergence for Quantum Channel Coding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/18r82hcfyff4y",
  "venue": "arXiv",
  "versions": []
}