{
  "abstract": "In the Kronecker product C2⊗CN, completely entangled subspaces (CESs) are subspaces containing no nonzero product vectors. In this paper, we study the extension of a given M-dimensional CES to a higher-dimensional CES. We first prove an existence result using the geometry of the Segre variety and an incidence-variety dimension-counting argument. In particular, an M-dimensional CES can be extended to an (M+1)-dimensional CES whenever M<N−1. We then introduce a constructive method based on matrix representations and invertible local transformations. We show that if the corresponding matrix Ψ satisfies rank(Ψ)≤N−2, an explicit extension can be constructed. In particular, the condition 2M≤N−2 is sufficient for this construction. Finally, we give a concrete example in C2⊗C8, where a three-dimensional CES is extended to a four-dimensional CES.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Imperial College London, London SW7 2AZ, UK",
    "Department of Electronics, Beijing Jiaotong University, Beijing 100044, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Yunlang Li"
    },
    {
      "affs": [
        1
      ],
      "name": "Ziwei Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ee7g97hbe2h0d.bib",
  "cited_by": 0,
  "doi": "10.3390/math14214050",
  "fulltext_url": null,
  "id": "ee7g97hbe2h0d",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/4050",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/ee7g97hbe2h0d.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:47Z",
      "native_id": "10.3390/math14214050",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/4050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Extensions of Completely Entangled Subspaces in C2⊗CN",
  "title_text": "Extensions of Completely Entangled Subspaces in C2⊗CN",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T00:21:04Z",
  "url": "https://research.draconitic.com/paper/ee7g97hbe2h0d",
  "venue": "Mathematics",
  "versions": []
}