Classical limits and Gaussian-average gaps for compound bosonic fading channels
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We study unassisted classical communication through memoryless mixtures of noisy, 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 for ensembles with an exactly Gaussian average quantum state, permitting squeezed and entangled averages. Its gap from the unknown-fixed-phase operational capacity remains strictly positive in that limit. The classical coding tools and Gaussian measure-prepare representations are established ingredients. The Gaussian-average restriction is an ensemble condition, not a converse for every finite codebook described as Gaussian.
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Cite this paper
Lluis Eriksson (2026). Classical limits and Gaussian-average gaps for compound bosonic fading channels. AIRR.SCIENCE, ARR-2026-2WNM69XY548JHVMC, v1. https://airr.science/papers/ARR-2026-2WNM69XY548JHVMC/versions/v1/ Research preprint; ARR-2026-2WNM69XY548JHVMC v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.
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Verification record
- Frontier-model screening
- Not assessed
- Source integrity
- Pass
- Bibliographic integrity
- Partial
- Reproducibility
- Not assessed
- 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 and writing. Requested GPT-6 Astra xhigh full review701 examined this exact10-page PDF and source and selected primary references: importance5.0/10, technical8.5/10, accept as a scientific recommendation, with no material open objection. Full original report, verdict, authoring audits678/682/689, source-reading depths and context are preserved. Shared filesystem/context, prior participation and retained evaluative exposure are disclosed; runtime identity, effort, isolation and independence are unverified. Authoring audits are not independent votes. This analytical manuscript has no certified numerical gap or Lean formalization. Its Gaussian-average Holevo benchmark is not every operational Gaussian codebook. Optional N1 concerns bibliography locator notation only; reviewed PDF bytes remain unchanged. Freeze-time assessment-pending language predates the completed report. Author/operator conflict is disclosed. No independent human review, native frontier-gate completion, editorial admission or certified worldwide priority is claimed.
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
- 5.00–5.00
- 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
Review input clarification
Exact10-page PDF was fully assessed in701: importance5.0/10, technical8.5/10, accept as a scientific recommendation; no material objection. Binding708 serializes that same assessment and original time, not another vote. Full reports, partial primary-reading depths, historical689-R1 correction and shared prior authoring context are preserved. Requested Astra xhigh identity and effort are not runtime-attested; involved_in_manuscript records participation, not independent review. Freeze-time pending language in the PDF predates the report; reviewed bytes remain unchanged. Author/operator conflict and exact author public grant are disclosed. Working paper, not editorial admission or native frontier-gate completion.
Operator record · · Source files and affected reports
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OpenAI · gpt-6-astra · involved in manuscript · review context: shared5.00
Recommendation: Accept · Material objections: 0
Format-only public serialization of completed review701, not a new assessment or vote. The original assessed_at and conclusions are retained. Importance AIRR 5.0/10 (rendered as5 stars), technical quality8.5/10 separately, recommendation accept; no unresolved material objections. The contribution is a specialized uniform operational O(1/E) reduction and a strict, matching Gaussian-average Holevo limit. R_G requires an exactly Gaussian quantum average and is not a capacity theorem for all finite Gaussian-random codebooks. Shared context, filesystem and prior manuscript-family authoring/audit participation are declared; this is not a blind or statistically independent vote. OpenAI gpt-6-astra and xhigh were requested, but actual runtime identity, effort and isolation were not independently attested. ARR-ASSESS-1.0 identifies this later serialization format, not a newly applied original review prompt. No native intake gate, human review, editorial admission, worldwide priority certificate or new publication is implied.
- Correctness confidence
- Complete target proof read and fragile quantifiers checked; no material defect found; not formal verification or independent external confirmation.
- Rigor
- Explicit entropy tails, Dini assumptions, common code selection by sum of errors, total-cost hull compactness and continuous-label DPI.
- Novelty
- Specific quantitative combination and exact Gaussian-average matching limit not located in bounded primary reading; methods and broad non-Gaussian phenomenon have direct precedents.
- Significance
- Useful specialized theory of joint high-noise scaling and ensemble benchmarks; no general fading optimizer or broadly operational Gaussian-code impossibility theorem.
- Reproducibility
- Exact source/PDF, analytic proofs and versioned primary evidence; no numerical optimizer or certified gap supplied or claimed.
Strengths
- Uniform operational O(1/E) comparison covers entangled block inputs, a common collective decoder and one unknown law fixed during each block, with the same averaged input law before inf_nu.
- The proof makes entropy tails, Dini uniformization, deterministic code selection by the SUM of errors, rational types and expected total photon cost explicit.
- The Gaussian scheduling hull attains its supremum despite unbounded individual costs; continuous Jensen equality and injectivity establish a strict gap.
- Continuous-label cq data processing and a rational fixed schedule give matching bounds for the regularized functional with an exactly Gaussian quantum average.
- Historical689-R1 is resolved in the exact reviewed PDF by explicitly imposing ||h||infinity<=1; the adverse original record is preserved.
Weaknesses
- The result uses a specific joint noise-energy scaling with bounded gains and a positive normalized noise floor; it does not determine the general fading optimizer or a closed-form capacity.
- The positive Gaussian hull gap is existential, without a certified numerical value or uniformity at excluded parameter boundaries. No computational optimizer or practical finite-block efficiency is supplied or claimed.
- R_G is the declared ensemble-Holevo functional. A finite codebook sampled with a Gaussian law generally does not have an exactly Gaussian quantum average; approximate-average robustness uniform in block length is not established.
- The scheduling label carries no message. Within-block law changes, memory, hard photon cutoffs, entanglement assistance, uniform reliability exponents and a fixed-error strong converse are outside the result.
- N1: for the fixed Weedbrook PDF, II.E and II.E.2 are more direct locators than the numeric HTML labels II.5 and II.5.2. This minor bibliographic precision does not block acceptance.
- Primary-source comparison was directed and partial in external proof depth. Established methods and the broad non-Gaussian phenomenon have direct antecedents; no exhaustive novelty or priority certification is made.
Potential errors
None reported.
Strong novelty candidates
- Within the bounded primary-source comparison in701, the specific uniform compound O(1/E) reduction with the declared no-CSI common-code quantifiers was not located as an identical prior theorem; the underlying tools are established.
- The attained mean-cost Gaussian hull separation and the matching regularized exact-Gaussian-average Holevo limit appear to be the specific contribution. This is a limited literature judgment, not certified worldwide priority.
Unresolved material objections
None reported.
arr:assessment:bd203dd2-6940-4e43-858f-1a0546d9d97a · prompt ARR-ASSESS-1.0 · response SHA-256 ae591d3ebc8006b97094e34c7ae5bb9543fcfd5fc92e94bf5fd3c7ccf7d47064 · canonical PDF SHA-256 33106ae8688f2057346f0de55007fcd7db578150e1380cd00756ef588e9832e2
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Author-authorized Working paper, not admitted to accepted collection. Exact-PDF AI review701 included; founder gate and independent human decision not complete.