{
  "abstract": "We prove dimension-independent Hyers--Ulam stability for surjective approximate isometries of the positive trace-class cone in both the trace and Bures metrics. Here $\\varepsilon\\geq0$ is a uniform upper bound on the additive error in preserving distances. Such an approximate isometry is uniformly approximated by a Wigner symmetry (a unitary or antiunitary conjugation), with error at most $9\\varepsilon/2$ in the trace metric and $2\\sqrt2\\varepsilon$ in the Bures metric, even if it does not fix zero. For maps fixing zero, the trace bound improves to $3\\varepsilon$ even under the hypothesis of $δ$-surjectivity, independently of $δ$. In infinite dimensions, we construct spectrum-preserving homeomorphisms of the full state space, including mixed states, whose distortions tend to zero in both metrics but which stay a fixed uniform distance from every Wigner symmetry. For state spaces, stability holds in each fixed finite dimension with a dimension-dependent modulus tending to zero as $\\varepsilon\\to0$, but no such modulus can be chosen independently of dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37133",
  "author_total": 1,
  "authors": [
    {
      "name": "Sam Looi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9gqn42h3fwqxg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37133",
  "fulltext_url": null,
  "id": "9gqn42h3fwqxg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37133",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214934559",
  "pdf_url": "https://arxiv.org/pdf/2609.37133",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9gqn42h3fwqxg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2609.37133",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37133"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Stability of isometries of quantum states",
  "title_text": "Stability of isometries of quantum states",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/9gqn42h3fwqxg",
  "venue": "arXiv",
  "versions": []
}