Constant-gap entanglement distillation and a spectral criterion for noise-universal communication
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We prove dimension-independent additive bounds on two-way entanglement distillation. For every conjugate local diagonal unitary invariant state, distillable entanglement, secret key and relative entropy of entanglement lie in an explicitly computable interval of width at most log2(5) bits per copy. For the broader class invariant under local diagonal signs, the diagonal-relative-entropy reference exceeds distillable entanglement by at most log2(9). The proof uses established partial breeding with a stopped classification whose entropy is bounded independently of dimension; a reduction-based seed pays for all initial assistance. The resulting recovery bound also implies at most log2(6) ebits of irreversibility for any mixture of a pure state and separable noise, without a marginal constraint, and controls mixtures with a mixed maximally correlated component. For an identity component mixed with arbitrary channel noise, we give six capacity guarantees and reduce their simultaneous worst cases to depolarizing channels. An explicit isotropic interval has absolute width tending to 2(1-f) at fixed entangled fraction f, refining the known relative large-dimension approximation. For general discrete Hamiltonians with a finite partition sum at some temperature, we identify the exact spectral boundary of absolute entanglement-assisted recovery: for each fixed reset state, the loss vanishes precisely when the partition sum diverges at its critical inverse temperature. In that regime all six capacities attain their erasure benchmarks with absolute o(1) loss. In the complementary regime every fixed reset has a strictly positive limiting assisted deficit, given by a critical-Gibbs variational formula. An explicit integer spectrum has an exact constant-loss plateau. The reset may have infinite energy or entropy. Oscillator consequences include reversible distributed states and a vanishing classical arbitrary-partner additivity defect. Optimal constants, efficient implementations and general exact finite-energy capacities remain unresolved.
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Cite this paper
Lluis Eriksson (2026). Constant-gap entanglement distillation and a spectral criterion for noise-universal communication. AIRR.SCIENCE, ARR-2026-58XZ9SCZA39DSRF0, v1. https://airr.science/papers/ARR-2026-58XZ9SCZA39DSRF0/versions/v1/ Research preprint; ARR-2026-58XZ9SCZA39DSRF0 v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.
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Version history
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Verification record
- Frontier-model screening
- Not assessed
- Source integrity
- Pass
- Bibliographic integrity
- Pass
- Reproducibility
- Pass
- Lean 4
- Not applicable
Recorded under ARR-VERIFY-1.0. AIRR verification and screening are not peer review.
AI assistance statement
Substantial OpenAI Codex assistance with research, proofs, drafting and computational checks. GPT-6 Astra xhigh was requested; the same model reviewer was involved in prior proof audits and manuscript revisions. Its explicit assessment of this exact final PDF is accept, technical quality 9/10 and AIRR importance 7/10, with no unresolved material or minor objection. That final assessment uses documented unchanged scientific evidence and an exact minor-revision check; it is not a claimed new full reading, rerun, blind review or additional independent vote. Historical reports and their artifact identities are preserved. Runtime identity and memory/filesystem isolation are not independently attested. No independent human peer review, formal verification or exhaustive priority certification 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
- 7.00–7.00
- 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; Benchmark match incomplete
OpenAI · gpt-6-astra · involved in manuscript · review context: unknown7.00
Recommendation: Accept · Material objections: 0
Accept the exact candidate-6-minor-1 PDF identified above. The closed assessment assigns technical quality 9/10 and AIRR importance 7/10; only the latter is millennium_score and overall_stars. Dimension-independent absolute distillation bounds and a spectral criterion for recovery of six erasure benchmarks are supported within the stated operational hypotheses. For finite critical partition, the positive all-reset limiting deficit characterized exactly is EA. No material or minor objection remains unresolved. This object faithfully serializes the existing assessment dated above; it is not a new review or an additional independent vote. The same model reviewer participated in the research and earlier reviews. No fresh context isolation, new full reading, new visual inspection or recalculation is claimed. model_id records the requested GPT-6 Astra configuration with xhigh effort; actual runtime identity is not independently attested.
- Correctness confidence
- The documented complete review and exact-revision follow-up found no material error; support, infinite-entropy, mixed-encoder, privacy and nonattainment steps were audited. All three minor corrections were verified. This is strong review confidence, not formal or independent human verification.
- Rigor
- The accepted arguments explicitly account for paid entanglement seeds, Eve's purification and public transcript, finite logical registers, expected energy, countably decomposable LOCC, and spectral converses without an inapplicable Gibbs hypothesis. Technical quality was separately assessed at 9/10.
- Novelty
- Substantive candidates are the absolute dimension-independent distillation losses and the operational spectral criterion with an all-reset EA deficit. Critical Gibbs entropy, reduction, partial breeding, hashing, twirling, known capacity formulas and Petz sufficiency are credited dependencies. Priority searches were targeted, not exhaustive.
- Significance
- Absolute distillation intervals, noise-universal communication applications and a sharp spectral boundary constitute exceptional potential on the AIRR scale, supporting 7/10. General capacity functions, efficient implementations and externally demonstrated field-shaping impact remain absent; the evidence does not justify 8/10.
- Reproducibility
- The prior review documented artifact hashes, complete 24-page visual inspection, exact reproduction of new mathematical data and explicit reuse of identical evidence. The follow-up verified unchanged scripts/results and resolved metadata traceability. Serialization adds no numerical runs or fresh PDF inspection.
Strengths
- The stopped-classification protocol pays for its entanglement seed and supplies absolute losses independent of dimension, with distinct CLDUI, LDOI and pure/separable consequences.
- The communication applications distinguish minimax statements from bounds for every noise channel and keep channel capacities separate from entanglement costs of states.
- The spectral section treats nonattainment, finite-register continuity, arbitrary fixed reset density including infinite entropy, and positive EA loss through an explicit variational formula.
- Operational and bibliographic dependencies are identified; artifact comparison, numerical reproduction and correction tracking support a traceable exact-version assessment.
Weaknesses
- The proof is dense and combines delicate coding and infinite-dimensional arguments. The review is by the same involved model, without formal proof certification, independent human replication or independently attested runtime identity.
- Novelty is a reasoned candidate assessment based on targeted primary-source checks, not exhaustive priority certification. Importance is potential; external or experimental impact has not been established.
- The asymptotics concern each fixed reset, not uniform convergence over all reset states or arbitrary input-dependent infinite-dimensional noise. The two-way infinite-dimensional claims use expected block-average cost and countably decomposable LOCC.
- Finite critical partition gives the exact limiting positive EA deficit, not formulas for the other quantum/private/two-way deficits. General finite-energy capacities, depolarizing quantum/private capacity, efficient receivers, strong converses and second-order results remain outside scope.
- Numerical diagnostics verify finite algebra and reproducibility, not operational coding/security theorems or infinite-dimensional limits. Engineered spectra identify a mathematical boundary, not an observed experimental phase transition.
Potential errors
None reported.
Strong novelty candidates
- Stopped classification with paid entanglement and an absolute dimension-independent loss, including its CLDUI/LDOI interval consequences.
- Absolute isotropic and noise-universal communication bounds, distinguished from established symmetry reductions and relative asymptotic estimates.
- Recovery of six erasure benchmarks for every arbitrary fixed reset density under critical partition divergence.
- A positive limiting EA deficit for every fixed reset under critical partition finiteness, with an exact finite-energy variational characterization.
Unresolved material objections
None reported.
arr:assessment:5962f2de-c224-4013-b350-a43a4a170a7c · prompt ARR-ASSESS-1.0 · response SHA-256 80375e44bf97a2176af9375c1a3b4931615f7a73b06e3d881982603fa8d94c88 · canonical PDF SHA-256 6636559ebb4d478ebc7af7aff29c72e54b98cd56093b5a0ed1b1dcaf03692994
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Author-authorized exact-version Working paper; author is AIRR operator. Favorable model assessment is not an AIRR editorial acceptance or independent human peer review. No unresolved material or minor objection in the preserved exact-version model assessment.