{
  "abstract": "The Wigner entropy conjecture posits that pure Gaussian states minimize the Shannon entropy of non-negative Wigner functions, known as the Wigner entropy. We show that mixing a specific pure Wigner-negative state with another suitably chosen quantum state can restore Wigner positivity while retaining a Wigner entropy that is slightly - but strictly - below the vacuum entropy. As a consequence, we disprove the Wigner entropy conjecture, as well as the stronger Wigner majorization conjecture, by deriving simple analytical counterexamples with violations of the entropy bound no larger than $10^{-3}$. Such states with sub-vacuum Wigner entropy can be found arbitrarily close to the vacuum and can also exhibit sub-vacuum Wigner-Rényi $α$-entropy for $0<α<2$. We identify the physical mechanism behind the existence of such states, which arises from a subtle interplay between the uncertainty principle and non-Gaussianity. The key idea of this paper was developed with the help of AI tools, building on the characterization of extreme non-negative Wigner functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24670",
  "author_total": 3,
  "authors": [
    {
      "name": "Zacharie Van Herstraeten"
    },
    {
      "name": "Nicolas J. Cerf"
    },
    {
      "name": "Ulysse Chabaud"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ff1rq0saxfvpc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24670",
  "fulltext_url": null,
  "id": "ff1rq0saxfvpc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24670",
  "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",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7214013026",
  "pdf_url": "https://arxiv.org/pdf/2609.24670",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ff1rq0saxfvpc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24670",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24670"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Wigner-positive quantum states can have lower entropy than the vacuum",
  "title_text": "Wigner-positive quantum states can have lower entropy than the vacuum",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/ff1rq0saxfvpc",
  "venue": "arXiv",
  "versions": []
}