{
  "abstract": "We construct PPT states on $\\mathbb{C}^m \\otimes\\mathbb{C}^n$ that have Schmidt number asymptotically approaching the smaller local dimension. More specifically, we construct a PPT state with Schmidt number at least $$ \\left\\lceil \\frac{m + n - ((m - n)^2 + 4(m + n - 1))^{1/2}}{2} \\right\\rceil. $$ In the case of equal local dimensions ($m = n$), this becomes $n - \\lfloor(2n - 1)^{1/2}\\rfloor$, far exceeding the previous constructions which achieved $n/2 + O(1)$. In the case of unequal local dimensions, our result shows that there exists a PPT state on $\\mathbb{C}^n \\otimes \\mathbb{C}^{3n-4}$ with Schmidt number at least $n-1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11849",
  "author_total": 2,
  "authors": [
    {
      "name": "Nathaniel Johnston"
    },
    {
      "name": "Benjamin Lovitz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/egmyttndjwgnf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11849",
  "fulltext_url": null,
  "id": "egmyttndjwgnf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11849",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.11849",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/egmyttndjwgnf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.11849",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11849"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "PPT states of almost maximal Schmidt number",
  "title_text": "PPT states of almost maximal Schmidt number",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/egmyttndjwgnf",
  "venue": "arXiv",
  "versions": []
}