{
  "abstract": "The space of $n\\times n$ density matrices is the full state space of an $n$-level quantum system. While it has been asserted in the literature on quantum information theory that decomposing this state space into equirank pieces yields a Whitney stratification, rigorous proofs have remained absent. Using methods from invariant theory, this work provides a proof that the rank decomposition of the matrix algebra constitutes a (b)-regular stratification in the sense of Whitney. Furthermore, we demonstrate how the Uhlmann connection - which describes the adiabatic holonomy of mixed states and reduces to the Berry connection on pure states - can be geometrically treated as a stratified connection on a stratified vector bundle. Finally, our appendix provides a self-contained exposition of stratified fiber bundles and the new concept of stratified connections, which may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02773",
  "author_total": 3,
  "authors": [
    {
      "name": "Howy Jordan"
    },
    {
      "name": "Markus J. Pflaum"
    },
    {
      "name": "Gerd Rudolph"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1e3jjce64b96.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02773",
  "fulltext_url": null,
  "id": "d1e3jjce64b96",
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  "landing_url": "https://arxiv.org/abs/2610.02773",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
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      "arxiv",
      "math.DG"
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      "3107|Quantum Mechanics and Applications"
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  "openalex": "W7220473161",
  "pdf_url": "https://arxiv.org/pdf/2610.02773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1e3jjce64b96.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.02773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Stratification of the space of density matrices via invariant theory and Uhlmann's connection",
  "title_text": "Stratification of the space of density matrices via invariant theory and Uhlmann's connection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/d1e3jjce64b96",
  "venue": "arXiv",
  "versions": []
}