{
  "abstract": "Shor conjectured that a von Neumann measurement attains the accessible information of every binary quantum ensemble. We prove the conjecture constructively in arbitrary finite dimension. For every finite-outcome positive operator-valued measure (POVM) $M$, we form an operator $T_M$ from the posterior label probabilities and show that its spectral projection-valued measure (PVM) $Π_M$ satisfies $I_{Π_M}(X{:}Y)\\ge I_M(X{:}Y)$; every rank-one refinement retains the inequality. Two applications of Jensen's operator inequality prove the comparison and yield an exact concave variational formula for the accessible information. The result is a special case of the general theorem of Fang, Fawzi, and Fawzi on measured $f$-divergences; the proof below isolates the binary argument and makes the replacement $M\\mapsto T_M\\mapstoΠ_M$ explicit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19003",
  "author_total": 1,
  "authors": [
    {
      "name": "Sunghyeon Jo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bd7mftq7kav36.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19003",
  "fulltext_url": null,
  "id": "bd7mftq7kav36",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19003",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19003",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bd7mftq7kav36.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.19003",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19003"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Shor's Conjecture Is True: Projective Measurements Suffice for Binary Accessible Information",
  "title_text": "Shor's Conjecture Is True: Projective Measurements Suffice for Binary Accessible Information",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/bd7mftq7kav36",
  "venue": "arXiv",
  "versions": []
}