{
  "abstract": "High-dimensional bipartite entanglement depends on how probability is distributed across the Schmidt spectrum, whereas a single reference-state fidelity resolves only one spectral scale. We develop multiscale Schmidt-spectrum bounds that connect geometric measures with quantitative Schmidt-number witnesses. For any partition of a pure-state Schmidt spectrum, several nested Vidal tails determine block masses. We derive the sharp upper boundary of the associated normalized nuclear-norm coordinate and show that equality holds if and only if the spectrum is uniform within each block. Refining the partition gives a monotone hierarchy of tighter bounds whenever the added tail data distinguish unequal block means. We also solve a relaxed weighted multiscale optimization globally: one scalar parameter specifies its unique full-support optimizer and explicit value on the nontrivial branch. Using the established single-tail fidelity--resource curve as a baseline, we obtain exact-fidelity equality refinements, convex-roof lower bounds for mixed states, and quantitative calibrations of Schmidt-number witnesses. A higher-tail relation further bounds convex-roof extended negativity in terms of Vidal tails and identifies the pure-state equality spectra. Leakage-aware and joint-confidence formulations state how these bounds can be used with incomplete data. Multistep tails require block-resolved or independently certified spectral information; they are not determined by one projector expectation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21209",
  "author_total": 6,
  "authors": [
    {
      "name": "Liang Xiong"
    },
    {
      "name": "Zhixiang Jin"
    },
    {
      "name": "Yanling Wang"
    },
    {
      "name": "Wei Chen"
    },
    {
      "name": "Hong Tao"
    },
    {
      "name": "Nung-sing Sze"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0keab4r1qfbdy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21209",
  "fulltext_url": null,
  "id": "0keab4r1qfbdy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21209",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7213905063",
  "pdf_url": "https://arxiv.org/pdf/2609.21209",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0keab4r1qfbdy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2609.21209",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21209"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Multiscale Schmidt-Spectrum Bounds for High-Dimensional Entanglement: Geometric Measures and Schmidt-Number Witnesses",
  "title_text": "Multiscale Schmidt-Spectrum Bounds for High-Dimensional Entanglement: Geometric Measures and Schmidt-Number Witnesses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:03Z",
  "url": "https://research.draconitic.com/paper/0keab4r1qfbdy",
  "venue": "arXiv",
  "versions": []
}