{
  "abstract": "We revisit the Segawa--Suzuki spectral mapping theorem for abstract Szegedy-type quantum walks from a block-encoding viewpoint. Retaining both eigenspaces of the involution underlying the chiral symmetry yields a natural two-by-two block representation in which the usual discriminant operator and its counterpart form the diagonal blocks. The non-endpoint spectral mapping theorem then follows from an elementary Schur decomposition, substantially simplifying the original proof by avoiding its invariant-subspace decomposition and approximate-eigenvector arguments. The same framework establishes the result for the spectrum, point spectrum, and Fredholm essential spectrum and gives a direct block-theoretic description of the endpoint inherited and birth eigenspaces. We illustrate the construction with a one-dimensional split-step quantum walk.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00498",
  "author_total": 1,
  "authors": [
    {
      "name": "Yohei Tanaka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0mnfzw41grz1q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00498",
  "fulltext_url": null,
  "id": "0mnfzw41grz1q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00498",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00498",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0mnfzw41grz1q.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00498",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00498"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A block-encoding approach to the Segawa-Suzuki spectral mapping theorem",
  "title_text": "A block-encoding approach to the Segawa-Suzuki spectral mapping theorem",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0mnfzw41grz1q",
  "venue": "arXiv",
  "versions": []
}