{
  "abstract": "We study divisibility of finite-dimensional quantum dynamics in the Heisenberg picture when the dynamical maps need not be invertible. Heisenberg divisible dynamics determines unique reduced propagators on the accessible operator systems, and Heisenberg CP-divisibility is shown to be equivalent to an operator-norm monotonicity. Although each reduced propagator admits a unital completely positive extension, independently chosen extensions need not satisfy a composition law. Generalized inverses restore this law algebraically, but do not, in general, preserve complete positivity. We characterize the resulting obstruction and give a sufficient construction based on unital completely positive projections onto the accessible operator systems. It is shown that for qubit dynamics Heisenberg CP-divisibility always guarantees a completely positive generalized-inverse propagator. Finally, we analyze time-local generators at singular times and identify the associated gauge freedom on dynamically inaccessible directions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07986",
  "author_total": 2,
  "authors": [
    {
      "name": "Federico Settimo"
    },
    {
      "name": "Dariusz Chruściński"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4gj97521q8gh0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07986",
  "fulltext_url": null,
  "id": "4gj97521q8gh0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07986",
  "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": "W7220932623",
  "pdf_url": "https://arxiv.org/pdf/2610.07986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4gj97521q8gh0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07986"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Divisibility of Non-Invertible Quantum Dynamics in the Heisenberg Picture",
  "title_text": "Divisibility of Non-Invertible Quantum Dynamics in the Heisenberg Picture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/4gj97521q8gh0",
  "venue": "arXiv",
  "versions": []
}