{
  "abstract": "Let $\\mathbb{P}_n$ be the cone of $n\\times n$ complex positive definite matrices. For $0<θ<1$ and $r\\ge0$, let $M_r^{(θ)}$ denote the weighted matrix power mean, with the logarithmic endpoint at $r=0$, defined by $$ M_r^{(θ)}(A,B) = \\begin{cases} \\big((1-θ)A^r+θB^r\\big)^{1/r}, & r>0,\\\\[2mm] \\exp\\big((1-θ)\\log A+θ\\log B\\big), & r=0. \\end{cases} $$ For $p>q\\ge0$, we introduce $$ Φ_{p,q}^{(θ)}(A,B) = \\operatorname{Tr}\\big[M_p^{(θ)}(A,B)-M_q^{(θ)}(A,B)\\big]. $$ We prove that $Φ_{p,q}^{(θ)}$ is a quantum divergence in the sense of Bhatia-Gaubert-Jain. Moreover, for $$ 0\\le q\\le1\\le p\\le2,\\qquad p>q, $$ it is jointly convex and satisfies the data processing inequality for completely positive trace-preserving maps, with the output side interpreted by the regularized boundary convention whenever it is singular. The construction recovers Hellinger-type and Jensen-Shannon-type quantities as special cases or limits. We also compute the induced local quadratic form and provide scalar and matrix obstructions showing that the convexity and data-processing range cannot be extended to all parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06870",
  "author_total": 4,
  "authors": [
    {
      "name": "Trung Hoa Dinh"
    },
    {
      "name": "Minh Toan Ho"
    },
    {
      "name": "Ha Trang Nguyen"
    },
    {
      "name": "Trung Dung Vuong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0m2av20271ve8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06870",
  "fulltext_url": null,
  "id": "0m2av20271ve8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06870",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7221045970",
  "pdf_url": "https://arxiv.org/pdf/2610.06870",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0m2av20271ve8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.06870",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06870"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weighted Two-Parameter Quantum Divergences Generated by Matrix Power-Mean Gaps",
  "title_text": "Weighted Two-Parameter Quantum Divergences Generated by Matrix Power-Mean Gaps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/0m2av20271ve8",
  "venue": "arXiv",
  "versions": []
}