{
  "abstract": "Electromagnetic duality in the toric code has order two at the level of anyon types and acts as a Hadamard-type logical transformation on the encoded quantum information. Here, we ask whether it can likewise be realized microscopically as an order-two Clifford operation. For the $\\mathbb{Z}_2$ toric code, we prove that any locality-preserving Clifford realization of electric-magnetic exchange cannot have order two. Our proof is fully general and requires neither translation symmetry with restricted families of system sizes nor a fixed pairing between vertex and plaquette stabilizers. Geometrically, the proof locally emulates the unavoidable crossing between electric and magnetic strings, similar to a cross-cap in a non-orientable manifold. Extending the problem to the $\\mathbb{Z}_N$ toric code, we find that an order-two Clifford realization exists for odd $N$, whereas it is impossible for even $N$. Our results show that the group law of an emergent electromagnetic duality need not lift faithfully to its microscopic Clifford realization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02097",
  "author_total": 3,
  "authors": [
    {
      "name": "Shunta Takahashi"
    },
    {
      "name": "Zhi Li"
    },
    {
      "name": "Beni Yoshida"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eshfxwgqvfppa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02097",
  "fulltext_url": null,
  "id": "eshfxwgqvfppa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02097",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
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      "arxiv",
      "hep-th"
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
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    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7216063456",
  "pdf_url": "https://arxiv.org/pdf/2610.02097",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eshfxwgqvfppa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02097",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02097"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A No-Go Theorem for Order-Two Clifford Electric-Magnetic Duality",
  "title_text": "A No-Go Theorem for Order-Two Clifford Electric-Magnetic Duality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/eshfxwgqvfppa",
  "venue": "arXiv",
  "versions": []
}