{
  "abstract": "We prove that the square root of the separable quantum optimal transport cost associated with the orthogonal projection onto the antisymmetric subspace defines a genuine distance between density matrices. Equivalently, this establishes the triangle inequality for the order-two Beatty-França quantum optimal transport construction induced by the Hilbert-Schmidt distance between pure states. The result also proves metricity of the corresponding distance derived from separable SWAP fidelity. The proof replaces the unavailable gluing argument by convex-roof duality and a dimension-independent interpolation result for Hermitian operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03769",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomasz Miller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1e57m7vg9dw7e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03769",
  "fulltext_url": null,
  "id": "1e57m7vg9dw7e",
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  "landing_url": "https://arxiv.org/abs/2609.03769",
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  "native_subjects": [
    [
      "arxiv",
      "math-ph"
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      "arxiv",
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  "pdf_url": "https://arxiv.org/pdf/2609.03769",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1e57m7vg9dw7e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.03769",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03769"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Metricity of separable quantum optimal transport with the Hilbert-Schmidt cost",
  "title_text": "Metricity of separable quantum optimal transport with the Hilbert-Schmidt cost",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1e57m7vg9dw7e",
  "venue": "arXiv",
  "versions": []
}