{
  "abstract": "We study nonconvex optimization of measured quantum $f$-divergences over rank-one projective measurements. For smoothly operator-Fenchel liftable generators and faithful states, every projective local maximum and every second-order stationary point is globally optimal over all POVMs. The criterion is blockwise: a critical PVM is optimal exactly when the compressed states are proportional on each equal-score block; otherwise an explicit two-vector rotation has positive ascent curvature. Operator-convex generators admit a positive atomic curvature resolution, and the quadratic $χ^2$ case yields two-sided residual bounds. For binary accessible information, this framework proves the known adaptive-capacity equality and shows that every nonidentical qubit ensemble has exactly two stationary projective measurements, proving conjectures of Keil and Thai--Dall'Arno. A rare-prior limit connects weighted Jensen--Shannon information to relative entropy and yields a finite counterexample to the proposed equivalence between observational-entropy and all-ensemble mutual-information orders. The landscape theorem also covers measured Rényi divergences of finite positive order and measured relative entropy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27767",
  "author_total": 1,
  "authors": [
    {
      "name": "Domingos S. P. Salazar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bny7p1c3phxgp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27767",
  "fulltext_url": null,
  "id": "bny7p1c3phxgp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27767",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7214183178",
  "pdf_url": "https://arxiv.org/pdf/2609.27767",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bny7p1c3phxgp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27767",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27767"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Benign Projective Landscapes for Measured Quantum Divergences",
  "title_text": "Benign Projective Landscapes for Measured Quantum Divergences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/bny7p1c3phxgp",
  "venue": "arXiv",
  "versions": []
}