[
  {
    "id": "ARR-2026-2WNM69XY548JHVMC-v3",
    "type": "article",
    "title": "Classical limits and learning gaps for compound bosonic fading channels",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          26
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-2WNM69XY548JHVMC",
    "version": "v3",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-2WNM69XY548JHVMC/versions/v3/",
    "note": "Research preprint; ARR-2026-2WNM69XY548JHVMC v3. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We study classical communication over noisy mixtures of phase-insensitive bosonic Gaussian channels. Both thermal noise and photon budget scale with an energy parameter. An explicit measure-prepare representation converts every quantum block code, including entangled codewords and collective receivers, into a classical code with identical error and an exactly quantified cost increment. The same simulation works for an unknown fixed mixing law. A Gaussian-smoothing estimate and a uniform finite-alphabet reduction give an explicit O(E^-1) comparison with a classical compound variational value. This value optimizes one input distribution before taking the worst mixing law. We also prove a strict separation between classical optimal modulation and the time-sharing hull of Gaussian coherent modulations for a matched-reset example. Matching bounds determine the high-energy limit of a regularized Holevo functional with Gaussian average marginals. A block-uniform, energy-controlled continuity modulus removes both exact marginal Gaussianity and Gaussianity of the full average state. We prove that almost every product coherent Gaussian random codebook from a fixed finite deterministic schedule has the required approximate marginals, controlling empirical moments separately. Strict cost slack or an explicit common rescaling enforces physical feasibility. This yields an operational converse for reliable sequences in the defined typical class, below an unrestricted non-Gaussian common-code rate at sufficiently large energy. It does not assert a good decoder for every random book or cover every protocol described as Gaussian. The same explicit classical comparison extends to free prior entanglement. For a finite compound family with classical feedback the limiting value instead optimizes after the worst law is fixed. A matched-reset/AWGN pair has a strict learning gap: one feedback bit after a zero-photon pilot eventually outperforms arbitrary prior entanglement without feedback. The Gaussian, coding and continuity tools used in the argument have established antecedents."
  }
]