{
  "abstract": "We investigates the joint compatibility problem of the three pairwise concurrences, the three-tangle, and the Kempe invariant in arbitrary pure three-qubit states, and gives necessary and sufficient conditions for these five quantities to be simultaneously realizable by the same pure state. This five-dimensional compatibility region can be viewed as a fiber structure over the previously derived four-dimensional reachable region. We further find that the residual continuous local-unitary freedom depends on the position of the state within this region. In the generic interior, one continuous degree of freedom remains. It is fixed if the three-tangle vanishes or a pairwise concurrence becomes zero, and also at the boundary of the four-dimensional tangle region. The Kempe invariant gives the simplest algebraic parametrization of the fifth coordinate, but the same degree of freedom may be described by a known pure-state entanglement monotone. The compatibility conditions can also be expressed in terms of concurrence-based bipartite measures and multipartite quantities fixed by the pairwise concurrences and the three-tangle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03864",
  "author_total": 3,
  "authors": [
    {
      "name": "Wei Song"
    },
    {
      "name": "Xiao-Lan Zong"
    },
    {
      "name": "Ming Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5817qxtrm8xyz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03864",
  "fulltext_url": null,
  "id": "5817qxtrm8xyz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03864",
  "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": "W7208712310",
  "pdf_url": "https://arxiv.org/pdf/2609.03864",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5817qxtrm8xyz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.03864",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03864"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Five-Dimensional Compatibility and Stratified Local-Unitary Structure of Pure Three-Qubit States",
  "title_text": "Five-Dimensional Compatibility and Stratified Local-Unitary Structure of Pure Three-Qubit States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/5817qxtrm8xyz",
  "venue": "arXiv",
  "versions": []
}