[
  {
    "id": "ARR-2026-5A13QJ5MZ98GWVFB-v1",
    "type": "article",
    "title": "Nilpotent noise and complete reverse data processing",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          27
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-5A13QJ5MZ98GWVFB",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-5A13QJ5MZ98GWVFB/versions/v1/",
    "note": "Research preprint; ARR-2026-5A13QJ5MZ98GWVFB v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We give a sufficient criterion for a reverse relative-entropy comparison valid after adjoining any finite-dimensional quantum reference. It combines a completely positive trace-nonincreasing nilpotent noise map, CP domination on the image of a channel, and a positive invertible output filter. A finite polynomial inverse replaces a small-perturbation assumption and yields an explicit coefficient independent of reference dimension. Applications include amplitude-damping channel comparisons and a three-level finite-height noise family. We also construct rational full-rank separable two-qubit states proving that the complete mutual-information contraction coefficient of each nonconstant amplitude-damping channel equals one, although its ordinary relative-entropy contraction is strict. The witnessing information vanishes in the limit. The result obstructs one sufficient capacity construction; it does not establish a capacity-additivity theorem or an optimal complete coefficient."
  }
]