{
  "abstract": "The additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every Rényi order $p>1$, at the von Neumann point $p=1$, and for sufficiently small positive $p$, while much of the interval $0<p<1$ has remained open. In this work, we prove that for every $p>0$ there exist finite-dimensional quantum channels whose minimum output $p$-Rényi entropies violate additivity. Our proof combines two constructions: random projection-induced channels yield nonadditivity for $p>3/4$, and antisymmetric postprocessing extends the violation to all positive Rényi orders. Our estimates also improve the output-dimension bound obtained by Belinschi, Collins, and Nechita for additivity violation of minimum output von Neumann entropy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.15210",
  "author_total": 4,
  "authors": [
    {
      "name": "Debbie Leung"
    },
    {
      "name": "Benjamin Lovitz"
    },
    {
      "name": "Ion Nechita"
    },
    {
      "name": "Peixue Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9wjq7k0jbx9st.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.15210",
  "fulltext_url": null,
  "id": "9wjq7k0jbx9st",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.15210",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7169625508",
  "pdf_url": "https://arxiv.org/pdf/2607.15210",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9wjq7k0jbx9st.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2607.15210",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.15210"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Counterexamples to additivity of minimum output $p$-Rényi entropy of quantum channels for all $p\\ge 0$",
  "title_text": "Counterexamples to additivity of minimum output p-Rényi entropy of quantum channels for all p≥ 0",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/9wjq7k0jbx9st",
  "venue": "arXiv",
  "versions": []
}