[
  {
    "id": "ARR-2026-2GTKNVK5QM9H8BFR-v1",
    "type": "article",
    "title": "Universal optimal tests of unknown unitary dynamics: determinant exponents and tensor stability",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          16
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-2GTKNVK5QM9H8BFR",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-2GTKNVK5QM9H8BFR/versions/v1/",
    "note": "Research preprint; ARR-2026-2GTKNVK5QM9H8BFR v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We study forward-query tests of an arbitrary fixed unitary channel against memoryless noise with unknown fixed input and output rotations. A Schur-Weyl reduction gives a family of optimal candidate tests, but leaves a channel-dependent minimization over partitions. We remove that minimization: the balanced partition is optimal simultaneously for every channel, every query number and every compact alternative family, even against adaptive and more general positive physical testers. A Gaussian Kraus-matrix identity and classical majorization yield the universal optimizer, exact determinant error exponents, polynomial finite-query bounds, and a sharp rank threshold for perfect detection. For qubits, the spin-flip spectrum determines all even-query errors. Using classical noncommutative-rank theory, we characterize stability of perfect detection under every tensor partner by a shrunk-subspace condition. A completely depolarizing partner of dimension d-1 destroys perfect detection whenever this condition fails. For the qutrit Werner-Holevo channel we compute exact exponents after adjoining the smallest possible partner, a depolarizing qubit, and for its tensor square. The independent unknown rotations, memoryless calls, unrestricted retained reference and enlarged global-unitary null in the tensor examples are essential."
  }
]