{
  "abstract": "Entanglement and nonstabilizerness capture distinct aspects of quantum complexity, yet their relation through the entanglement spectrum remains poorly understood. Here we develop a spectral framework for bipartite nonlocal nonstabilizerness. We introduce a generalized anti-flatness and derive upper and lower bounds on the nonlocal stabilizer Rényi entropy (SRE) in terms of Rényi entanglement entropy and spectral non-uniformity. We further reduce the local-unitary optimization to a single-unitary problem and prove that the ordered Schmidt reference state is a local minimum of the SRE for integer $α\\geq2$. Applying these results to exponentially and algebraically decaying spectra reveals parametrically distinct relations between entanglement and nonlocal nonstabilizerness. For broad spectra, we introduce a dyadic-shell sandwich construction that determines the asymptotic SRE scaling. At one-dimensional conformal critical points, it yields a universal hierarchy of double-logarithmic scaling laws for integer $α\\geq2$. Our spectral bounds and dyadic-shell sandwich construction provide general tools for analyzing nonlocal SRE, offering a flexible framework that can be applied to a wide range of entanglement spectra in quantum many-body systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01993",
  "author_total": 2,
  "authors": [
    {
      "name": "Lei-Yi-Nan Liu"
    },
    {
      "name": "Jian Cui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fksbv602e5nj7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01993",
  "fulltext_url": null,
  "id": "fksbv602e5nj7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01993",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7207698520",
  "pdf_url": "https://arxiv.org/pdf/2609.01993",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fksbv602e5nj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.01993",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01993"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum",
  "title_text": "Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/fksbv602e5nj7",
  "venue": "arXiv",
  "versions": []
}