{
  "abstract": "We connect the structure theorem for quasiprobability representations to quantum error correction. For a code space invariant under a subgroup of an extended Weyl-Heisenberg group, the Brif-Mann construction gives a semi-functorial representation whenever its kernel satisfies the Stratonovich-Weyl axioms, and composes on channels covering full error-correction cycles. With phase-space parity available, a kernel other than the ordinary Wigner one exists iff the code space is invariant under a lattice of displacements: among compact-phase-space bosonic codes, this is only the ideal Gottesman-Kitaev-Preskill family; in finite dimension, this is every qudit stabiliser code, whose negative volume for odd prime dimension is the syndrome-averaged logical magic. For rotation-symmetric, one-photon, non-Pauli qudit and spin codes only the ordinary kernel remains, its negativity reflecting the physical carrier, not logical content; a sector-graded representation built from recovery isometries restores a resource reading. We add a channel atlas, a closed-form magic lifetime under displacement noise, a Kirkwood-Dirac layer, and finite-energy corrections.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Rev. Res. 8, 043076. (2026)",
  "arxiv": "2607.02164",
  "author_total": 2,
  "authors": [
    {
      "name": "Enrico Bozzetto"
    },
    {
      "name": "Jonte R. Hance"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cg39qcashwaxj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.02164",
  "fulltext_url": null,
  "id": "cg39qcashwaxj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.02164",
  "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",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.02164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cg39qcashwaxj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2607.02164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.02164"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Phase-Space Representations of Quantum Error-Correcting Codes",
  "title_text": "Phase-Space Representations of Quantum Error-Correcting Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/cg39qcashwaxj",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/7my9-zgfz",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}