{
  "abstract": "A quantum walk is a mathematical model and a quantum version of a random walk. For the past two decades, it has been studied from mathematical and physical viewpoints. It has many desirable properties. This paper reevaluates quantum walk from a quantum mechanical perspective, as Feynman essentially proposed it as a toy model in his path integral method. Then we demonstrate that the quantum walk model exhibits both particle-like and wave-like properties by showing reflection and partial reflection as a particle and interference as a wave. In particular, for an initial state supported at two sites $\\pm\\ell$, we explicitly derive the weak limit distribution of the Hadamard walk and show that the Konno distribution is modulated by the interference factor $2\\cos^2(\\ell k(x))$. The resulting interference profile is reminiscent of far-field (Fraunhofer-type) diffraction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26204",
  "author_total": 4,
  "authors": [
    {
      "name": "Norio Konno"
    },
    {
      "name": "Shigeki Matsutani"
    },
    {
      "name": "Etsuo Segawa"
    },
    {
      "name": "Tomoyuki Terada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56kecn6ttb6dk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26204",
  "fulltext_url": null,
  "id": "56kecn6ttb6dk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26204",
  "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"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7223071621",
  "pdf_url": "https://arxiv.org/pdf/2610.26204",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56kecn6ttb6dk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.26204",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26204"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Wave-Particle Complementarity in Quantum Walk from a Quantum Mechanical Perspective",
  "title_text": "Wave-Particle Complementarity in Quantum Walk from a Quantum Mechanical Perspective",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/56kecn6ttb6dk",
  "venue": "arXiv",
  "versions": []
}