{
  "abstract": "In Heo and Kiem (2019), the authors raised a problem relating integral zeros of binary Krawtchouk polynomials, parametrized by quadruples $(m,n,k,\\ell)$ with $m\\le n$ and $k\\le \\ell$, to the existence of pairs of subspaces satisfying the range criterion in quantum information theory, and settled the symmetric case $k=\\ell$. In this paper, we solve the problem for the following three asymmetric families: $(m,n,k,\\ell)=(3,t^2-1,t(t-1)/2,t(t+1)/2)$, $t\\ge2$; $(m,n,k,\\ell)=(4,3t^2+2t-1,(3t^2-t)/2,(3t^2+5t+2)/2)$, $t\\ge2$; $(m,n,k,\\ell)=(4,3s^2+4s,(3s^2+s)/2,(3s^2+7s+4)/2)$, $s\\ge1$. The remaining cases are sporadic zeros, with only finitely many for each $m\\ge5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08518",
  "author_total": 3,
  "authors": [
    {
      "name": "Jaeseong Heo"
    },
    {
      "name": "Young-Hoon Kiem"
    },
    {
      "name": "Chul-hee Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1w9enyqfmmvnh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08518",
  "fulltext_url": null,
  "id": "1w9enyqfmmvnh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08518",
  "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/2611.08518",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1w9enyqfmmvnh.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:04Z",
      "native_id": "2611.08518",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08518"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Integral zeros of Krawtchouk polynomials and quantum entanglements",
  "title_text": "Integral zeros of Krawtchouk polynomials and quantum entanglements",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:04Z",
  "url": "https://research.draconitic.com/paper/1w9enyqfmmvnh",
  "venue": "arXiv",
  "versions": []
}