{
  "abstract": "We study the recently developed theory of quantum convolution for discrete-variable quantum systems. We classify the discrete quantum convolutional channels generated by an invertible $2\\times2$ coupling matrix and a fixed environmental state according to which entries of the coupling ma- trix vanish. Under role-preserving basis relabelings, matrices with all four entries nonzero form $d-2$ canonical cross-ratio classes, whereas matrices with exactly one vanishing entry split into four inequivalent branches. We determine the optimized one-shot Holevo information and the classical, quantum, and private capacities for all four one-entry-vanishing branches. If a diago- nal entry vanishes, the channel is an entanglement-breaking measure-and-prepare orbit channel: its classical capacity equals a relative entropy coherence of the environmental state, whereas its quantum and private capacities vanish. If an off-diagonal entry vanishes, the channel is a degradable generalized-dephasing channel: one complete orthonormal basis is transmitted without error, whereas the quantum and private capacities are determined by the entropy deficit of the environ-ental state after dephasing in the conjugate basis. Thus, the position of a single vanishing entry selects two qualitatively different communication regimes. When all four entries are nonzero, the channels are irreducibly Weyl covariant, reducing the classical-capacity problem to a regularized minimum-output-entropy problem. For the unique fully nonzero coupling class in the single-qutrit case, we further derive an exact Holevo formula for a depolarized one-parameter family and identify its entanglement-breaking threshold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16200",
  "author_total": 1,
  "authors": [
    {
      "name": "Chunhe Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9p2xafr5bpat6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16200",
  "fulltext_url": null,
  "id": "9p2xafr5bpat6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16200",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7213418800",
  "pdf_url": "https://arxiv.org/pdf/2609.16200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9p2xafr5bpat6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16200"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Coupling Structure Determines Communication Regimes in Discrete Quantum Convolutional Channels",
  "title_text": "Coupling Structure Determines Communication Regimes in Discrete Quantum Convolutional Channels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/9p2xafr5bpat6",
  "venue": "arXiv",
  "versions": []
}