{
  "abstract": "Higher-order quantum transformations allow multiple channel uses to be combined through different causal architectures, from parallel and fixed-order sequential networks to general higher-order processes. Whether this causal freedom improves channel transformation when the higher-order operation is also constrained by a resource theory remains largely unexplored. We study this question in the dynamical resource theory of coherence using a unified semidefinite-programming framework. For two qubit amplitude-damping channels and the identity target, we prove a strict causal hierarchy at every nontrivial damping strength under both maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC). In contrast, mixed-Pauli channels admit a common teleportation simulation that transfers the channel dependence to Bell-diagonal program states prepared in parallel. The remaining processing can then be absorbed into a single quantum operational, so parallel, fixed-order sequential, and general higher-order strategies achieve the same optimal error for any target. These results identify free program-state parallelisation as a structural obstruction to causal enhancement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08639",
  "author_total": 6,
  "authors": [
    {
      "name": "Lin Zhu"
    },
    {
      "name": "Benchi Zhao"
    },
    {
      "name": "Xuanqiang Zhao"
    },
    {
      "name": "Ranyiliu Chen"
    },
    {
      "name": "Xin Wang"
    },
    {
      "name": "Shenggen Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70mmfq3tazbp6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08639",
  "fulltext_url": null,
  "id": "70mmfq3tazbp6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08639",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7212041076",
  "pdf_url": "https://arxiv.org/pdf/2609.08639",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70mmfq3tazbp6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:52Z",
      "native_id": "2609.08639",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08639"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Causal-Class Hierarchies in Coherence-Constrained Channel Transformation",
  "title_text": "Causal-Class Hierarchies in Coherence-Constrained Channel Transformation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:52Z",
  "url": "https://research.draconitic.com/paper/70mmfq3tazbp6",
  "venue": "arXiv",
  "versions": []
}