Classical limits and learning gaps for compound bosonic fading channels
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
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.
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Cite this paper
Lluis Eriksson (2026). Classical limits and learning gaps for compound bosonic fading channels. AIRR.SCIENCE, ARR-2026-2WNM69XY548JHVMC, v3. https://airr.science/papers/ARR-2026-2WNM69XY548JHVMC/versions/v3/ Research preprint; ARR-2026-2WNM69XY548JHVMC v3. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.
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Version history
The paper identifier remains stable. Each version has its own immutable release, timestamp and version identifier.
Revision statement
Major revision. Extend the same paper to prior entanglement and per-law adaptive backward feedback; prove a matched-reset/AWGN learning separation with zero-photon training. Preserve full exact-PDF review754 including its lower importance4.5, technical8.5, significance reservations and minor clarifications; v1/v2 and their own reports remain immutable.
Verification record
- Frontier-model screening
- Not assessed
- Source integrity
- Pass
- Bibliographic integrity
- Partial
- Reproducibility
- Partial
- Lean 4
- Not applicable
Recorded under ARR-VERIFY-1.0. AIRR verification and screening are not peer review.
AI assistance statement
The named author directed substantial OpenAI Codex assistance in derivation, writing and numerical work. Full requested GPT-6 Astra xhigh review754 examined this exact18-page PDF and full source: importance4.5/10, technical8.5/10, accept with minor clarifications as a scientific recommendation, zero material mathematical objections and zero required theorem/proof repairs. All adverse significance findings, original report/verdict, context, chronology and authoring audits716/745 are retained. Reviewer analysis preceded consultation of authoring audit745, which is not an independent vote. Shared filesystem, family participation and reused authoring context are declared; effective runtime identity, effort, isolation and independence remain unverified. Later public binding only serializes754 without regrading. Three minor clarifications are supplied in a separate author/operator notice, leaving evaluated PDF bytes unchanged. The PDF pending-assessment statement predates completion of754. The result assumes joint high-signal/high-noise scaling; prior entanglement is free and finite per block; feedback direct coding concerns finite compound families with per-law adaptive cost. The learning separation uses a capacity-matched AWGN gain and is existential; no numerical gap or energy threshold is supplied. Typical Gaussian-book results require the stated finite schedule, reliability and physical cost conditions. No formal proof, certified worldwide priority, independent human review or goal>7 achievement is claimed. Author/operator conflict and founder-authored status are disclosed. Working paper, not admission to the accepted collection or native model gate completion. Earlier public versions and their own grades remain immutable.
Frontier-model screening
Status: not_assessed. Any listed reports correspond to this exact version under ARR-SCREEN-1.0; no absent assessment is represented as a pass.
Model assessments and review context
- Distinct models
- 1
- Range
- 4.50–4.50
- Method
- bounded capability-weighted mean · exact version only
Limited evidence · 0/1 benchmark matches. This is an evidence description, not a probability of correctness.
Only one distinct model; One provider; shared blind spots possible; Fresh blinded review context not documented for every model; Mathematical benchmark not applied to this subject; Adverse reports or unresolved objections require editorial disposition
Review input clarification
The complete18-page v3 received actual full review754: importance4.5/10, technical8.5/10, accept with minor clarifications, zero material mathematical objections and zero required theorem/proof repairs. The official minor_revision enum preserves this recommendation. Five overall stars are only half-up display of4.5, never a new5.0grade. Format-only binding761 is not another review or vote. All adverse significance findings remain: established minimax/training antecedents, implicit capacity-matched gain, uncomputed learning gap/energy threshold, joint signal/noise scaling and restricted typical Gaussian-book class. Three optional clarifications appear in author-clarifications.txt without changing the PDF. A separately sourced bibliographic-name correction concerns the review itself; the full original report remains unchanged. Initial reviewer analysis preceded consultation of authoring audit745; that audit is not independent review. Shared files/context and same-family participation are disclosed; actual requested Astra xhigh runtime/effort/isolation/independence are not verified. assessed_at uses the original MANIFEST754 review-record assembly marker, not a verified exact response-completion second. The PDF pending-assessment paragraph predates754. Ordinary linked author deposit, exact public release grant, founder authorship and author/operator conflict are recorded. Working paper, not native gate completion, author-editor acceptance or independent human admission. v1/v2 and their distinct5.0/5.5 importance assessments remain unchanged. The goal>7 remains unmet.
Operator record · · Source files and affected reports
- operator-binding-notice.txt · SHA-256
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OpenAI (requested; runtime unverified) · gpt-6-astra (requested; runtime identity and xhigh effort unverified) · unknown · review context: shared4.50
Recommendation: Minor Revision · Material objections: 0
Format-only serialization of completed review 754 of this exact 18-page PDF; no new scientific review, vote or regrading. Original recommendation: Accept with minor clarifications for a specialist venue, subject to ordinary independent editorial review. Importance remains 4.5/10; five whole stars is only the official half-up display, not a new 5.0 grade. Technical quality remains 8.5/10. No material mathematical objection or required theorem/proof repair was identified. The strongest contribution combines uniform quantitative bosonic-to-classical bounds with a strict Gaussian scheduling-hull gap and robust marginal/typical-book consequences. General compound minimax and feedback-training mechanisms have strong antecedents; the constructed learning gap and energy threshold are uncomputed. GPT-6 Astra xhigh was requested; effective runtime identity, effort, isolation and independence remain unverified. Own unscored notes preceded consultation of authoring audit 745 in shared filesystem context. assessed_at uses the observed 754 record-assembly timestamp, not an exact response-completion time; ARR-ASSESS-1.0 denotes this later serialization. The scientific recommendation is not independent human review, a correctness certificate or an editorial admission.
- Correctness confidence
- Substantive arguments checked; no located counterexample, but no formal verification or independent replication.
- Rigor
- Energy, quantifiers, compactness, decoder universality and finiteness explicit.
- Novelty
- Plausible new quantitative combination and Gaussian restriction results using established ingredients; no exhaustive priority certification.
- Significance
- Specialist value under narrow scaling; strict gap is existential and uncomputed.
- Reproducibility
- Frozen source and explicit proofs; no numerical gap or threshold calculation.
Strengths
- The original review found the explicit law-uniform O(1/E) bosonic-to-classical comparison technically sound within its joint signal/noise scaling, with a common compound decoder and quantified cost increment.
- The matched-reset argument separates the unrestricted optimum from the attained full Gaussian scheduling hull, including displaced, anisotropic and singular planar Gaussians; it closes a time-sharing loophole.
- Moment matching and an explicit continuity bound support robust one-mode marginal restrictions with unequal coordinate energies. Typical independent Gaussian books are treated with separate empirical-moment control and physical cost repair.
- The assisted section consistently treats arbitrary finite-per-block preshared entanglement with growing dimension, actual receiver quantum memory, finite mutual information and adaptive expected budgets separately at every law.
Weaknesses
- General compound minimax order, finite-family feedback training and strict finite compound gaps have primary antecedents; Section 7 is not a new general resource principle.
- The learning pair has an AWGN gain defined implicitly through an uncomputed reset capacity; neither its positive gap nor useful finite-energy threshold is evaluated.
- The uniform classical limit assumes fixed bounded gain and positive normalized-noise floor in a simultaneous signal/noise scaling.
- Typical independent Gaussian-book restrictions do not establish arbitrary Gaussian-protocol optimality or decoder achievability.
- Optional editorial clarification, source lines 54-125: Write 0 <= K < infinity explicitly; nonempty Gamma already entails nonnegativity. This is not a mathematical blocker or required proof repair.
- Optional editorial clarification, source lines 126-180: Replace ambiguous lower-channel wording by channel used for the lower bound or W-plus. This is not a mathematical blocker or required proof repair.
- Optional editorial clarification, source lines 1141-1219: Give Boche et al. PDF Theorem 1 / HTML Theorem 3.1 locators together. This is not a mathematical blocker or required proof repair.
- An evaluated positive gap/threshold and physically motivated fading family would increase usefulness; not required for the stated existence theorem.
- The original importance judgment did not find the conceptual reach, generality, quantitative application evidence or demonstrated downstream impact needed to justify AIRR excellence, exceptionality or field-changing importance. The retained 4.5/10 is not an average of technical diagnostics.
Potential errors
None reported.
Strong novelty candidates
- The original bounded literature comparison did not locate an exact antecedent to the complete uniform compound bound together with an attained strict Gaussian scheduling hull, marginal robustness and typical-book consequence. This is a plausible quantitative combination, not a certified worldwide-priority claim.
- The constrained bosonic learning construction is a useful explicit realization with law-by-law energy accounting. Its general minimax/training mechanisms and existence of strict compound resource gaps have antecedents; it is not a new general resource principle.
Unresolved material objections
None reported.
arr:assessment:16d3809e-e5d0-4d89-aedb-828ab341c07d · prompt ARR-ASSESS-1.0 · response SHA-256 b960c457693f95e445af6c6cf9623a3bdb4d537066d26ad90d54902f10650da2 · canonical PDF SHA-256 66176e7f21d2a4785b2355f07b3dcc49d4d4d3b8f93ebd36efe19d9a51537881
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Author-authorized founder-authored Working-paper v3, exact-PDF review754 retained with importance4.5, technical8.5 and minor clarifications. No author-editor acceptance, native gate completion or independent human approval. Earlier public versions remain unchanged.