{
  "abstract": "The non-stabilizerness, or \"magic\", of a quantum state is a common metric for the hardness of simulation on a classical computer, and is often quantified by the stabilizer Rényi entropy (SRE). We show how random superpositions of classically simulable states saturate the SRE to the symmetry-restricted Haar-random maximum. For any large-$N$ random pure-state ensemble satisfying the conditions of Schur's lemma, the average SRE of the $m$-component superposition $\\langle M_2(m)\\rangle=N-\\log_2[\\langle W(m)\\rangle]$ is governed by an average witness $\\langle W(m)\\rangle$ that universally decomposes into a Haar floor and an ensemble-specific excess. As the number of components $m$ increases, the excess is suppressed, resulting in a logarithmic scaling of the SRE before plateauing at the Haar-valued maximum. We derive a general closed form for $\\langle W(m)\\rangle$ in the thermodynamic limit, and numerically verify our result for random stabilizer states and random Gaussian states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22476",
  "author_total": 4,
  "authors": [
    {
      "name": "Joshuah T. Heath"
    },
    {
      "name": "Andrew Urilyon"
    },
    {
      "name": "Damien Quinn"
    },
    {
      "name": "Graham Kells"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4rr9e7932nqex.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22476",
  "fulltext_url": null,
  "id": "4rr9e7932nqex",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22476",
  "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",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7222961551",
  "pdf_url": "https://arxiv.org/pdf/2610.22476",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4rr9e7932nqex.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.22476",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22476"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Typical Superpositions are Magical",
  "title_text": "Typical Superpositions are Magical",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/4rr9e7932nqex",
  "venue": "arXiv",
  "versions": []
}