Sharp entropy budgets for communication with unknown resets and optical loss
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We study quantum reset channels with oscillator input energy E, unrestricted reset orientation and energy, and only a Renyi entropy budget B(E) on the reset state. For each fixed finite entropy order, we characterize when the flagged-erasure entanglement-assisted benchmark is recovered with uniform absolute error tending to zero: 2^B/E tends to zero below order one, B/log2(E+1) tends to zero at order one, and B tends to zero above order one. The sufficient conditions recover four communication benchmarks with one encoder and decoder for the entire fixed-noise compound class. For Shannon and fixed super-Shannon budgets we determine the full bounded entanglement-assisted minimax loss curves, uniformly in every finite budget. Known-noise and unknown-fixed-noise losses coincide asymptotically. We extend these curves to a quantum-limited attenuator in the transmitted branch, uniformly over transmissivities bounded away from zero, with one assisted code for unknown fixed attenuation and reset. Proofs combine spectral branch-information bounds, fixed finite compression, physical-energy type-subspace coding and an all-input converse. Finite-rank optical tests replace the pure-state test when transmission is mixed. Pointwise two-way recovery is treated separately using a cited distillation theorem. Parameters remain fixed throughout each code block, and the coding limit is taken at fixed E. No thermal-loss, arbitrary-variation or error-exponent theorem is asserted.
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Cite this paper
Lluis Eriksson (2026). Sharp entropy budgets for communication with unknown resets and optical loss. AIRR.SCIENCE, ARR-2026-7SWAJZ0X278GJ9NK, v1. https://airr.science/papers/ARR-2026-7SWAJZ0X278GJ9NK/versions/v1/ Research preprint; ARR-2026-7SWAJZ0X278GJ9NK v1. Not peer reviewed by AIRR.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.
- v1 · source snapshot available · viewing
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 Codex derivation, writing and numerical work. A complete exact-PDF review requested as GPT-6 Astra xhigh completed after the PDF freeze: importance 4.5, technical contribution 5.5, minor revision. Preparatory audits reused context; the full review used shared files and did not receive prior reports or a target grade. Runtime identity and isolation are not independently attested. The full report, minor comments and subsequent same-hash publication binding are retained separately. The freeze-time statement that no full assessment had yet been obtained is historical, not the current assessment status.
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
OpenAI · gpt-6-astra · unknown · review context: shared4.50
Recommendation: Minor Revision · Material objections: 0
Later same-SHA publication binding of the full review598, not a fresh or independent assessment and not an additional scientific vote. ARR-ASSESS-1.0 labels this later format, not an asserted original prompt invocation. The original review supports the stated entropy thresholds and uniform all-budget assisted minimax laws, including the optical mixed-signal test and common-code quantifier, within its declared scope; no unresolved material objection was identified. Research importance/overall remain 4.5/10; technical contribution remains 5.5/10; minor_revision and R1-R3 remain. Overall 5 stars is only the schema half-up rendering of 4.5. Unchanged full report SHA256 8e6a539ba20ed5c6ba0fc0581cd3dd1199e4287d0fa51f7eecfa02f92adfd504; unchanged original verdict SHA256 23bc933b633f6b0898ed9ddeb0c4eae1728c604da5c8b1d4d3b1ebd702ac2d79. This binding supplements and does not replace them. Shared context/files are retained; independence is unknown. OpenAI/gpt-6-astra labels record the requested model (xhigh), not runtime attestation. The original review saw the manuscript prior-audit disclosure and an incidental nonnumeric antecedent-status snippet, unused in scoring; no earlier grades were imported.
- Correctness confidence
- Nearest-integer schema rendering only: original 4.0/5 -> 4 stars; the original diagnostic mark is unchanged. The main proofs survived the original checks of quantifiers, endpoints, all-input converses and cited coding applicability. This was not formal verification or recursive proof of every antecedent.
- Rigor
- Nearest-integer schema rendering only: original 4.2/5 -> 4 stars; the original diagnostic mark is unchanged. The original review found explicit finite-dimensional reduction, physical cost accounting and uniform remainders. The two-way result retains a substantial separately cited working-paper dependency.
- Novelty
- Nearest-integer schema rendering only: original 3.6/5 -> 4 stars; the original diagnostic mark is unchanged. The operational entropy-budget minimax result and mixed-signal test appeared distinct from directly checked antecedents. The channel models, pure-loss benchmark, spectral-tail tools and compound coding theorems are established.
- Significance
- Nearest-integer schema rendering only: original 3.4/5 -> 3 stars; the original diagnostic mark is unchanged. The original judgment was a useful focused asymptotic contribution under restricted uncertainty, with no demonstrated practical blocklengths, broader-noise solution or field-changing importance.
- Reproducibility
- Nearest-integer schema rendering only: original 4.4/5 -> 4 stars; the original diagnostic mark is unchanged. The original review verified all 35 packet files and replayed all 6 programs with byte-identical outputs. No universal encoder/decoder was implemented; diagnostics do not establish capacity. No code was replayed for this binding.
Strengths
- Theorem 1: the original full review found the three fixed-entropy-order recovery thresholds supported by spectral tails, entropy-preserving truncation and admissible converse witnesses; necessity is established through assisted capacity, not independently for each unassisted capacity.
- Proposition 4/Lemma 3: exact type subspaces enforce physical input energy for every encoded state and support arbitrary-index compound coding with genuinely uninformed users. The private-rate environment/secrecy accounting and fixed-E-first limit were checked.
- Pointwise two-way sufficiency: the finite-codimension argument avoids infinite-energy forbidden-vector errors, and the cited distillation theorem includes seed payment. This remains an inherited pointwise result, not a common two-way code.
- Theorem 7: matching known-noise and compound assisted minimax loss curves were checked uniformly over all finite budgets, with an all-input converse and valid endpoint clipping; no thermal optimizer for the mixed channel was assumed.
- Theorem 8: the mixed-signal finite-rank Kraus-span detector, all-input entropy-deficit split, uniform kappa control including 1, and common code for unknown fixed (kappa,tau) survived the original audit; kappa remains bounded away from 0.
- Original evidence coverage: all 14 exact PDF pages, all 3 principal TeX files, supplement README/all 6 programs and declared primary theorem/proof passages were read; all 35 manifest files matched and all 6 diagnostic outputs replayed byte-identically. These are historical review598 checks, not new checks performed in binding605.
Weaknesses
- R1 (minor, documentary; retained): Reference [9], page 14, uses unversioned arXiv:1210.6926, resolved in the original audit to v2 dated 28 May 2013, while the bibliography says 2012. Pin v2 or distinguish first-submission year from version date. The cited theorem scope was sufficient; no material gap identified.
- R2 (minor, reproducibility; retained): supplement/README.txt names dependencies without versions. Record Python/NumPy/SciPy/mpmath versions. Preserve the limited diagnostic scope and distinguish independent_checks.py from independently attested human or isolated-model verification. The original six outputs reproduced exactly.
- R3 (minor, exposition; retained): Section 8.3/page 12 assembles the optical uniform error envelope across paragraphs. Consider one display collecting thermal truncation, branch-test bound, Shannon clipping or super-Shannon tail modulus, and q h(p_*)+h(z_E). Existing ingredients were checked for B/kappa uniformity; no missing estimate identified.
- Model-based mathematical assessment, not formal proof verification, human peer review, or correctness certificate.
- All manuscript sections reviewed; external primary references read to the stated depth, not in their entirety or recursively through all dependencies.
- The two-way conclusion depends on a substantive earlier working-paper distillation theorem; its relevant proof was inspected but not formally certified.
- Directed selective literature comparison cannot certify worldwide originality.
- No explicit compound encoder/decoder implemented or simulated; numerical diagnostics cannot establish capacity.
- No independent TeX rebuild; exact supplied PDF and source were read and visually compared.
- No guarantees beyond fixed parameters, fixed-E-first coding limit, assisted optical scope, and kappa bounded away from zero.
Potential errors
None reported.
Strong novelty candidates
- Qualified candidate from the original selective comparison: sharp operational entropy-budget recovery thresholds for orientation-unrestricted reset classes, beyond established Renyi spectral-tail tools and compound coding machinery. Worldwide originality was not certified.
- Qualified candidate from the original review: uniform all-budget known/compound assisted minimax laws and their optical extension with a mixed-signal test. The identity/replacement and optical/vacuum channel models, pure-loss benchmark and inherited working-paper ingredients are not claimed as new.
Unresolved material objections
None reported.
arr:assessment:db0b0d04-b907-44da-9eaa-6e14b5c4be2a · prompt ARR-ASSESS-1.0 · response SHA-256 8efb6dde484b8e4849f1e6d586d1b99cc69c635373d1575e4b22da2670406c08 · canonical PDF SHA-256 0b6572379ef56dd2d667cb52c768d55bd89ee7991545c3c186be92776aeb07c3
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Exact-version Working-paper release authorized through the author route and official operator handoff. The author is the AIRR operator and Codex acts on his instructions. This is not admission, independent human review or completion of the two-model founder admission gate.