{
  "abstract": "We study unital completely positive (UCP) maps on the finite Toeplitz operator system $\\mathcal T_d$ of $d \\times d$ Toeplitz matrices. We give an explicit characterization of pure UCP maps on $\\mathcal T_d$ taking values in $M_n$ in terms of positive $n\\times n$ matrix-valued trigonometric polynomials of degree at most $d-1$. This characterization yields a checkable criterion for deciding whether a given UCP map is pure. As an application, we prove that every pure UCP map on $\\mathcal T_d$ has a unique completely positive extension to the generated $C^*$-algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.02561",
  "author_total": 2,
  "authors": [
    {
      "name": "Ritul Duhan"
    },
    {
      "name": "Abhay Jindal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1adm62c2kqp3q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.02561",
  "fulltext_url": null,
  "id": "1adm62c2kqp3q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.02561",
  "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",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7163133715",
  "pdf_url": "https://arxiv.org/pdf/2606.02561",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1adm62c2kqp3q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2606.02561",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.02561"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "UCP Maps on Finite Toeplitz Systems",
  "title_text": "UCP Maps on Finite Toeplitz Systems",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1adm62c2kqp3q",
  "venue": "arXiv",
  "versions": []
}