[
  {
    "id": "ARR-2026-6FWR12DH3F8QBA5C-v1",
    "type": "article",
    "title": "Sharp determinant bounds for amplified antisymmetric channels and a noise law for noncommutative rank",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          16
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-6FWR12DH3F8QBA5C",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-6FWR12DH3F8QBA5C/versions/v1/",
    "note": "Research preprint; ARR-2026-6FWR12DH3F8QBA5C v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We study the largest normalized determinant in a Kraus matrix space after amplification by a completely depolarizing channel. For the three-dimensional antisymmetric channel, we prove a bound uniform in the auxiliary dimension, identify its exact value 2^(2/9)/4, and show that a finite amplification attains it if and only if its dimension is divisible by three. The proof balances a determinant maximizer, fixes its second and fourth singular-value moments, and uses a quadratic majorant of the logarithm. Combined with known unitary constructions, this determines the regularized value for every Holevo-Werner channel: dimension three is the unique exceptional case. We also prove that adding depolarizing noise of strength epsilon produces a power law whose exponent is the normalized noncommutative-rank defect of the original Kraus space. The latter estimate is uniform over all auxiliary dimensions and has a matching lower bound at one fixed finite dimension. These results sharpen finite-dimensional examples and an exact-rank criterion into, respectively, an infinite-amplification optimum and a quantitative noise law. We state the operational interpretation for tests of an unknown global unitary separately from free ancillary assistance."
  }
]