[
  {
    "id": "ARR-2026-5MAVBFTEF48DX8RT-v1",
    "type": "article",
    "title": "A complete class of optimal quantum tests for unknown unitary dynamics",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          16
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-5MAVBFTEF48DX8RT",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-5MAVBFTEF48DX8RT/versions/v1/",
    "note": "Research preprint; ARR-2026-5MAVBFTEF48DX8RT v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We consider repeated forward access to an unknown quantum channel. The null hypothesis is an arbitrary fixed unitary channel; the alternative is a memoryless channel whose input and output rotations are unknown but fixed across all uses. We prove a complete-class theorem: every physical positive tester is dominated, in orbit-averaged alternative acceptance and worst-case null acceptance, by a classical randomization of explicitly realizable parallel tests. The tests are indexed by partitions of the query number, prepare a maximally mixed representation register, entangle the multiplicity register with a reference, and measure return to that entanglement. Consequently, for any compact family of noise channels, the exact finite-query minimax problem reduces to a classical optimization over partitions. For one specified noise channel the complete error tradeoff is a minimum of explicit Choi-polynomial invariants. Adaptation and any larger positive-tester class containing parallel protocols give the same optimum. We derive the channel-independent optimal two-query test and its failure probability in terms of Choi purity and nonunitality. For complete depolarization we obtain the exact error at every dimension, query number and parallel reference dimension, recovering the known exponential benefit of multiplicity entanglement. We also give an error exponent for orthogonal random-unitary noise. The result requires both unknown rotations and memoryless uses; it does not establish parallel optimality for calibrated noise or arbitrary channel discrimination."
  }
]