{
  "abstract": "In this paper, we show that the generalized Bures--Wasserstein distance induced by the generalized fidelity fails the data processing inequality (DPI) in every dimension $n\\geq2$. In dimension two, we derive three sufficient conditions guaranteeing the DPI by using an explicit formula for the real part of the generalized fidelity. Furthermore, we find a necessary and sufficient condition under which the generalized fidelity reduces to the Uhlmann fidelity. We also show that neither the generalized Bures--Wasserstein distance nor its square is convex in one state, even with the other state and the reference fixed, in every dimension $n\\geq2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09753",
  "author_total": 3,
  "authors": [
    {
      "name": "Haobo Ma"
    },
    {
      "name": "Reza Rajaei"
    },
    {
      "name": "Wenlin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94bbqtdwkwrce.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09753",
  "fulltext_url": null,
  "id": "94bbqtdwkwrce",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09753",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7212136440",
  "pdf_url": "https://arxiv.org/pdf/2609.09753",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94bbqtdwkwrce.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2609.09753",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09753"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Generalized Fidelity, the Data Processing Inequality, and Convexity",
  "title_text": "Generalized Fidelity, the Data Processing Inequality, and Convexity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/94bbqtdwkwrce",
  "venue": "arXiv",
  "versions": []
}