{
  "abstract": "Given an open quantum system $S$ with environment $E$, we establish a one-to-one correspondence between completely positive trace-preserving (CPTP) maps from $S$ to $E$ and assignment maps initializing the composite system $SE$ in a possibly correlated state prior to unitary evolution. We show that every possible joint state $ρ_{SE}$ can be realized by such assignment maps, which are inherently Hermiticity-preserving and trace-preserving (HPTP). While these maps sacrifice global positivity, we derive a simple necessary and sufficient condition for any local state of $S$ to belong to their domain of validity. Furthermore, we prove that the geometry of this domain is governed by the joint state assigned to the maximally mixed input, ensuring that a non-zero volume of admissible local states can readily coexist with initial system-environment entanglement. Finally, we provide an operational protocol for witnessing such limits of validity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27338",
  "author_total": 2,
  "authors": [
    {
      "name": "James Fullwood"
    },
    {
      "name": "Weixiang Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgjrnwyg1kpqj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27338",
  "fulltext_url": null,
  "id": "bgjrnwyg1kpqj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27338",
  "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": "W7223090333",
  "pdf_url": "https://arxiv.org/pdf/2610.27338",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgjrnwyg1kpqj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27338",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27338"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Assignment maps for arbitrary reduced quantum dynamics",
  "title_text": "Assignment maps for arbitrary reduced quantum dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/bgjrnwyg1kpqj",
  "venue": "arXiv",
  "versions": []
}