{
  "abstract": "The Pauli-ball discrepancy, a quadratic discrepancy summed over all error radii, measures how uniformly the Pauli error images of a $K$-dimensional quantum code cover the $d$-dimensional Hilbert space. At parameters attaining equality in the quantum Singleton bound with minimum code distance $\\geq3$, or in the one-error Hamming bound with prime-power local dimension, the discrepancy of every projector of the prescribed rank equals an explicit benchmark plus an exact nonnegative remainder, which vanishes precisely for pure quantum maximum-distance-separable codes and nondegenerate perfect codes, respectively. For a Pauli ball of radius $e$ below half the target distance and size $V_e$, this remainder linearly bounds the squared Hilbert--Schmidt distance of the error-image Gram matrix from the identity. When $KV_e\\leq d$, it linearly bounds the diamond error and entanglement infidelity of a noise-independent polar recovery under any noise in that ball's span. For five qubits, we obtain the sharp rank-two Gram constant and exact logical channels of rotated codes attaining this linear order in diamond error. For pure states, the discrepancy equals a pure-state benchmark plus a positive weighted sum of marginal-purity defects, so absolutely maximally entangled states, when they exist, are exactly the minimizers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34399",
  "author_total": 1,
  "authors": [
    {
      "name": "Aryeh Lev Zabokritskiy \"Yohananov\""
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4nxggvwm1ejj4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34399",
  "fulltext_url": null,
  "id": "4nxggvwm1ejj4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34399",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7223790606",
  "pdf_url": "https://arxiv.org/pdf/2610.34399",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4nxggvwm1ejj4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34399",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34399"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Pauli-ball discrepancy and stability of quantum codes",
  "title_text": "Pauli-ball discrepancy and stability of quantum codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/4nxggvwm1ejj4",
  "venue": "arXiv",
  "versions": []
}