[
  {
    "id": "ARR-2026-2VT5B14BC88EG9TD-v1",
    "type": "article",
    "title": "Operational Signatures of Criticality from Petz Recovery: Collar-length Requirements in TFIM Exact Diagonalization",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          1,
          12
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-2VT5B14BC88EG9TD",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-2VT5B14BC88EG9TD/versions/v1/",
    "note": "Archived manuscript; ARR-2026-2VT5B14BC88EG9TD v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We study whether recovery-based operational distances exhibit a distinctive finite-size signature near quantum criticality. For a tripartition A-B-C of a 1D chain with a collar B of width w separating A from C, we compute a Petz-based reconstructed state and the recovery error E_Petz(w) = -log F (squared Uhlmann fidelity), and define an effective recovery distance d_eff(epsilon) as the minimal collar width achieving error below epsilon, stabilized by E_best(w) = min over w' <= w of E_Petz(w') and reported with explicit censoring. Using exact diagonalization of the transverse-field Ising chain at N = 11 with |A| = 2, we sweep hx across the critical region at hz = 0 and compare to a longitudinally perturbed control hz = 0.5: pronounced growth and extensive censoring of d_eff(epsilon) appear in the critical region at low temperature, while the control remains comparatively featureless; an extended-collar spot-check yields d_eff(1e-3) of about 7.6-7.7 at beta = 12 near hx in {0.96, 1.00}. v2 adds (no v1 result is changed): an explicit |C|-shrinkage caveat -- at fixed N, growing w also shrinks C, so the absolute scale of d_eff near w_max conflates buffer growth with a shrinking reconstruction target, while fixed-geometry comparisons across hx (the criticality signature) are unaffected; a window-relativity remark (epsilon, beta, N jointly set what is resolvable: at smaller N the beta = 12, epsilon = 1e-3 window censors even off-critical points, consistent with v1's own zoom); delivery of v1's \"future work\" item: a CMI-based distance computed on the same sweep shows the same criticality signature at its own threshold (CMI decays about half as fast as the Petz error, cf. 2601.0035); series positioning; and a fully regenerable verification suite."
  }
]