Complete contraction of unital qubit channels and order-constrained depolarization
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We determine the complete equal-reference contraction coefficients of the minimal quantum Fisher metric, its quadratic chi-square divergence and the finite triangular Petz divergence for every unital qubit channel. For a faithful normalized Choi state J, all three equal 1-16/Tr(J inverse); for singular J they equal one. An explicit qubit-qutrit lower family matches a harmonic-weight upper bound and gives the exact stabilization envelope, including a maximal factor of nine between coefficient suprema. For depolarization in dimension d, a commuting Bell family matches lambda^2 kappa/[1+lambda(kappa-1)] for each normalized nonaffine operator-convex Petz generator when 1<kappa<=d^2/2. A rank-two ladder extends SLD and triangular sharpness to kappa<=d(d+1)/2, using the actual reference marginal for the budget. We identify qubit classical-reference and separable/PPT restrictions throughout the physical noise range. A localized rational counterexample addresses one printed Doeblin equivalence, with its Hermitian primal and equality dual stated correctly. The results do not determine unrestricted BKM, relative-entropy, actual-mutual-information or capacity coefficients, and the lower constructions are not unitary phase models. Faithful limits, adverse controls, prior-work dependencies and model-review limitations are explicit.
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Cite this paper
Lluis Eriksson (2026). Complete contraction of unital qubit channels and order-constrained depolarization. AIRR.SCIENCE, ARR-2026-77DGRYDGXD8MDSY2, v2. https://airr.science/papers/ARR-2026-77DGRYDGXD8MDSY2/versions/v2/ Research preprint; ARR-2026-77DGRYDGXD8MDSY2 v2. Not peer reviewed by AIRR.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. Extends exact complete contraction to every unital qubit channel, proves the stabilization envelope and dimension-dependent order profiles, and corrects the Doeblin definition and NPT inference with preserved exact-PDF reviews.
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 canonical12-page PDF1041 was deposited as SUB-B8BF8FF049233864, private revision2 of SUB-DDD4EBE32883B252, and is released here as public v2 of the same record. Full review1031 concerns the pre-correction PDF1030 (SHA25650db4efe067fb88a0bef955d4e5b5779bc31a6afe4c1b78b0c16c9f518b89ab3). Its full adverse history is preserved. Corrective continuation1042 inspected this exact PDF1041 and resolved O1 (Hermitian Doeblin primal/equality dual) and O2 (NPT inference scope), explicitly reaffirming scientific importance5.8/10, global Millennium5.6/10 and technical quality8.5/10. These are distinct judgments; catalogue global5.6 is not technical8.5. This is ONE evaluation family, not two independent votes or automatic score inheritance. Requested GPT-6 Astra xhigh; effective model identity, effort, runtime isolation and independence are unattested. Codex participation, shared filesystem and reused context are disclosed. The original scientific recommendation accept means publication with declared scope, not editorial acceptance. Native distinct-identified-model admission gate remains incomplete and the record remains a Working paper. No later1033/1035/1037 claim or grade is imported. O3 bibliographic uncertainty, O4 limited operational scope/conditioning and O5 review-context limitations remain visible. The manuscript review-pending wording was frozen before1042 completed.
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
- 5.60–5.60
- 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
The canonical12-page PDF1041 was deposited as SUB-B8BF8FF049233864, private revision2 of SUB-DDD4EBE32883B252, and is released here as public v2 of the same record. Full review1031 concerns the pre-correction PDF1030 (SHA25650db4efe067fb88a0bef955d4e5b5779bc31a6afe4c1b78b0c16c9f518b89ab3). Its full adverse history is preserved. Corrective continuation1042 inspected this exact PDF1041 and resolved O1 (Hermitian Doeblin primal/equality dual) and O2 (NPT inference scope), explicitly reaffirming scientific importance5.8/10, global Millennium5.6/10 and technical quality8.5/10. These are distinct judgments; catalogue global5.6 is not technical8.5. This is ONE evaluation family, not two independent votes or automatic score inheritance. Requested GPT-6 Astra xhigh; effective model identity, effort, runtime isolation and independence are unattested. Codex participation, shared filesystem and reused context are disclosed. The original scientific recommendation accept means publication with declared scope, not editorial acceptance. Native distinct-identified-model admission gate remains incomplete and the record remains a Working paper. No later1033/1035/1037 claim or grade is imported. O3 bibliographic uncertainty, O4 limited operational scope/conditioning and O5 review-context limitations remain visible. The manuscript review-pending wording was frozen before1042 completed.
Operator record · · Source files and affected reports
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OpenAI · unattested (requested GPT-6 Astra xhigh; Codex participation) · involved in manuscript · review context: unknown5.60
Recommendation: Accept · Material objections: 0
Continuación correctiva1042 de la misma evaluación1031, sin reiniciar revisión completa ni constituir segunda voz/voto independiente. PDF1041 exacto de12p: O1 resuelta mediante primal hermítico/dual igualdad y distinción alpha_+; O2 resuelta al limitar BASE NPT a SLD/chi_min² y el par Petz a no-ambos-PPT. Intervalo de positividad explicitado sin ampliar teoremas. Tras diff y páginas afectadas, mantengo importancia5.8, global5.6 y técnica8.5 para este PDF por el mismo contenido y arquitectura demostrativa. Certificado Doeblin reproducido;1031 permanece íntegro. accept significa recomendación científica con alcance declarado, no aceptación editorial. Contexto compartido/participación Codex; identidad efectiva, esfuerzo e independencia no atestados.
- Correctness confidence
- O1/O2 resueltas en PDF1041. El examen general1031 y la comparación exacta sostienen las partes no cambiadas; control Doeblin reproducido. Sin prueba formal ni nueva voz independiente.
- Rigor
- Definición Doeblin e inferencia NPT precisadas; intervalo de positividad explícito. Permanecen las pruebas, restricciones y límites ordenados inspeccionados en1031.
- Novelty
- No hay teoremas nuevos ni nueva evidencia de prioridad. Candidatos de contribución y búsqueda dirigida de1031 conservan el mismo alcance y sus límites.
- Significance
- Fórmulas exactas y envolvente técnicamente útiles, con el mismo alcance especializado y ausencia de protocolo operacional o codificación unitaria demostrados.
- Reproducibility
- PDF/fuentes nuevos congelados, diff independiente,1031 íntegro, extracción exacta y certificado Doeblin reproducido. Inspectabilidad no atesta independencia.
Strengths
- O1/O2 corregidas exactamente; la definición y la inferencia corresponden ahora a las pruebas y fuente examinadas.
- Se conservan clasificación unital qubit, envolvente y perfiles de orden; la sección qubit es idéntica byte a byte.
- Intervalo alineado explícito incluye la rama negativa física y evita extender el límite fuera del dominio positivo.
- Hash/diff trazables y antecedente íntegro; control Doeblin exacto reproduce el resultado previo.
Weaknesses
- O3 conservada: bibliografía dirigida1031, prioridad abierta; no búsqueda nueva ni certificado de ausencia de teorema cubriente.
- O4 conservada: alcance especializado, testigos posiblemente mal condicionados, sin estabilidad experimental ni aplicación unitaria demostrada.
- O5 conservada: contexto952/998/1006/1010/1031 y filesystem compartidos, participación Codex y posible sesgo; no aislamiento o independencia verificados.
Potential errors
- O1/O2 permanecen como objeciones históricas del PDF1030; resueltas solamente para el PDF1041 comprobado. No se editan los informes anteriores.
- La exactitud de Bell para cada Petz no se extiende automáticamente a la franja rango dos; ni el supremo completo a cada R fijo. Estos límites permanecen expresos.
- Esta comprobación correctiva no repite las pruebas generales ni cinco replays de1031; no acredita cambios externos o candidatas posteriores1033/1035/1037.
Strong novelty candidates
- Clasificación completa de todo unital qubit con fórmula Choi y envolvente exacta, relativamente a las fuentes examinadas.
- Geometría de rango dos que amplía el rango exacto SLD/chi_min²/triangular hasta d(d+1)/2, diferenciada del rango Bell conocido.
Unresolved material objections
None reported.
arr:assessment:92f89170-e67d-4abb-9a21-6569b226e8ba · prompt ARR-ASSESS-1.0 · response SHA-256 eda53c393f3152e4ac8defa8268479e0647b84ca469a7dd9dfe9279f2b532149 · canonical PDF SHA-256 08efeffda4865e8f2f0b8e78bd0d2b6260c557a299cf5360d9aef1acc4062372
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Founder-authored Working-paper v2. Exact current report1042 and complete historical1031 report preserved as one evaluation family. Native admission gate incomplete; no Accepted status or independent human review.