{
  "abstract": "Indefinite causal order extends the conventional circuit paradigm by allowing local quantum operations to be connected without a predetermined global order. Within the process-matrix framework, it is characterized by causal nonseparability, whereas extensible causal separability (ECS) requires that, under arbitrary input-ancilla extensions, a process admit a recursive decomposition into components, each compatible with a particular operation acting first. Quantum circuits with classical control of causal order (QC-CC), in which previous outcomes dynamically determine which operation acts next, are known to generate ECS processes, but whether every ECS process admits such a realization has remained a longstanding open problem. We settle it through a generalized teleportation construction that realizes every multipartite ECS process as a QC-CC. We further establish consistency between ECS definitions for trivial and nontrivial global past and future systems. These results provide ECS with an exact operational interpretation and identify QC-CC as the complete circuit structure underlying this class of processes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18559",
  "author_total": 2,
  "authors": [
    {
      "name": "Wenjie Wei"
    },
    {
      "name": "Shengshi Pang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31qs4p2av1fd9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18559",
  "fulltext_url": null,
  "id": "31qs4p2av1fd9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18559",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.18559",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31qs4p2av1fd9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18559",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18559"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Extensibly Causally Separable Processes Admit Realizations as Quantum Circuits with Classical Control of Causal Order",
  "title_text": "Extensibly Causally Separable Processes Admit Realizations as Quantum Circuits with Classical Control of Causal Order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/31qs4p2av1fd9",
  "venue": "arXiv",
  "versions": []
}