[
  {
    "id": "ARR-2026-564FZ70CSN83KACD-v3",
    "type": "article",
    "title": "Common support and complete contraction with quantum side information",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          28
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-564FZ70CSN83KACD",
    "version": "v3",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-564FZ70CSN83KACD/versions/v3/",
    "note": "Research preprint; ARR-2026-564FZ70CSN83KACD v3. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "For a finite classical-quantum channel mapping i to tau_i, we prove that its complete equal-reference Umegaki contraction coefficient is one exactly when the intersection of the prepared-state supports is zero. The known positive-replacer bound supplies strict contraction in the complementary case. An operator-valued simplex factorization and a normalized graph projector give the converse with faithful separable hypotheses, uniform classical input, reference dimension equal to the input alphabet size and a joint binary readout. For every fixed channel, input, output and measured relative entropies tend to log 2. Two nonorthogonal pure outputs already exhibit the phenomenon: a certified finite binary retention exceeds the complete trace-distance coefficient, so a Hermitian Doeblin or trace bound cannot be substituted for the positive-replacer Umegaki bound. The graph effect can be nonseparable, and its convergence is not uniform over prepared states approaching equality. For classical outputs, a separate weight-independent Schur argument yields uniform convergence over all zero-Doeblin channels at fixed input size. We also determine exact SLD, minimal chi-square, triangular, BKM and Umegaki coefficients for symmetric classical channels, and distinguish binary input support from binary hypotheses or readout. Exponential conditioning, rare events, adaptive measurements and the quantum input denominator delimit the result. No capacity advantage, robust implementation, minimal reference dimension, general LOCC realization or worldwide priority is claimed."
  }
]