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pith:WX6FLUBH

pith:2026:WX6FLUBHM4ZJROUCMTBBXDLGCA

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Non-Invertible Symmetries on Tensor-Product Hilbert Spaces and Quantum Cellular Automata

Kansei Inamura, Rui Wen, Sakura Schafer-Nameki

Fusion category symmetries realizable on tensor-product Hilbert spaces must be weakly integral, with indices fixed by categorical data under defect assumptions.

arxiv:2605.15194 v1 · 2026-05-14 · cond-mat.str-el · hep-th · math.CT · quant-ph

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Claims

C1strongest claim

We show that, under certain physical assumptions on defects, any QCA-refined realization has QCA and symmetry-operator indices determined by the categorical data, up to the freedom of redefining the symmetry operators. We construct a lattice model that provides a QCA-refined realization for any weakly integral fusion category symmetry on a tensor product Hilbert space.

C2weakest assumption

The physical assumptions on defects that allow the indices to be determined solely by categorical data; without these the index determination may not hold.

C3one line summary

Any weakly integral fusion category admits a QCA-refined realization on tensor-product Hilbert spaces with QCA and symmetry indices fixed by the categorical data under defect assumptions.

References

68 extracted · 68 resolved · 16 Pith anchors

[1] Dua lity and defects in rational conformal ﬁeld theory 2007 · arXiv:hep-th/0607247

[2] On finite symmetries and their gauging in two dimensions, 2018

[3] ICTP Lectures on (Non-)Invertible Generalized Symmetries 2024 · arXiv:2305.18296

[4] What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Sym- metries 2023 · arXiv:2308.00747

[5] Lectures on Generalized Symmetries 2024 · arXiv:2307.07547

Formal links

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Cited by

1 paper in Pith

Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces

Receipt and verification

First computed	2026-05-17T21:40:25.031842Z
Last reissued	2026-05-17T21:57:18.429575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

b5fc55d027673298ba8264c21b8d661020c8c4bd0b1cb9d61e149e002a887ee2

Aliases

arxiv: 2605.15194 · arxiv_version: 2605.15194v1 · pith_short_12: WX6FLUBHM4ZJ · pith_short_16: WX6FLUBHM4ZJROUC · pith_short_8: WX6FLUBH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WX6FLUBHM4ZJROUCMTBBXDLGCA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b5fc55d027673298ba8264c21b8d661020c8c4bd0b1cb9d61e149e002a887ee2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cef356fed01486a70a11feb1010ff8920b58cc9e0a574ed2942670ccfbf9f25f",
    "cross_cats_sorted": [
      "hep-th",
      "math.CT",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.str-el",
    "submitted_at": "2026-05-14T17:59:45Z",
    "title_canon_sha256": "714999e6840e13897803c323bd51522e88a8e78e2f876440c0f23c72472a8492"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15194",
    "kind": "arxiv",
    "version": 1
  }
}