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 Not peer reviewed.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 they equal 1-16/Tr(J inverse); for singular J they equal one. A qubit-qutrit lower family matches a harmonic-weight upper and gives an exact stabilization envelope, including a maximal factor of nine between coefficient suprema. For dimension d depolarization, a commuting Bell family matches lambda^2 kappa/[1+lambda(kappa-1)] for each normalized nonaffine operator-convex Petz generator up to kappa=d^2/2. A principal-rich rank-two ladder extends SLD and triangular sharpness to kappa=d(2d-1)/2, with actual-marginal budgets and reference dimension 2d-1. A separate logarithmic calculation yields the complete equal-reference BKM and finite Umegaki lower lambda^2 P/[1+lambda(P-1)], P=d(d-1), with a constrained profile and four interval-certified finite comparisons. We also identify qubit classical-reference and separable/PPT restrictions and give a localized Doeblin counterexample. These results do not determine unrestricted BKM, Umegaki, actual-mutual-information or capacity optima; the displayed lower is not a unitary phase model. Faithful limits, prior dependencies, adverse controls and review-context limits 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, v3. https://airr.science/papers/ARR-2026-77DGRYDGXD8MDSY2/versions/v3/ Research preprint; ARR-2026-77DGRYDGXD8MDSY2 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 Not peer reviewed by AIRR.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. Extends the exact order range to d(2d-1)/2 and proves separate BKM/Umegaki lower bounds with full exact-PDF assessment and certified finite comparisons.
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
Full review1048 examined this exact15-page PDF1047 (SHA256 f805a688fb62e9bb34f4c8f107f906c4f85613f831cfda424d1805b797fffe07), read the complete manuscript and sources, reconstructed the proofs and reproduced five checkers plus own controls. It recommends scientific publication with declared scope and no unresolved material objections. Scientific importance6.1/10, global Millennium5.9/10 and technical quality8.7/10 are separate judgments, not an average. The catalogue global5.9 is not technical8.7. R1-R6, prior-art uncertainty, near-singular conditioning, lack of a general BKM upper or actual-MI/capacity result and optional presentation issue remain visible. Closure incidentI6 is preserved with the full report and history: a manifest-vs-extra-auxiliary assertion was corrected without changing inputs or scientific judgment. Requested GPT-6 Astra xhigh; effective identity, effort, runtime isolation and independence are unattested. Codex participation, reused952/998/1006/1010/1031/1042 context and shared filesystem are disclosed.1044 is a dependent technical audit, not another current manuscript vote;1031/1042 evaluated different predecessor PDFs and their full reports are historical, not score inheritance. Native accept is the scientific recommendation, not editorial Accepted status. The exact author revision3, clean scanner, CC-BY-4.0 permission/CC0 metadata and founder conflict are recorded. Public v3 remains a Working paper with the distinct-identified-model gate incomplete. Post-start1051/1052 and1054 are excluded from this PDF and assessment. The full-assessment-pending wording in the PDF describes its frozen status before1048 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
- 5.90–5.90
- 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
Full review1048 examined this exact15-page PDF1047 (SHA256 f805a688fb62e9bb34f4c8f107f906c4f85613f831cfda424d1805b797fffe07), read the complete manuscript and sources, reconstructed the proofs and reproduced five checkers plus own controls. It recommends scientific publication with declared scope and no unresolved material objections. Scientific importance6.1/10, global Millennium5.9/10 and technical quality8.7/10 are separate judgments, not an average. The catalogue global5.9 is not technical8.7. R1-R6, prior-art uncertainty, near-singular conditioning, lack of a general BKM upper or actual-MI/capacity result and optional presentation issue remain visible. Closure incidentI6 is preserved with the full report and history: a manifest-vs-extra-auxiliary assertion was corrected without changing inputs or scientific judgment. Requested GPT-6 Astra xhigh; effective identity, effort, runtime isolation and independence are unattested. Codex participation, reused952/998/1006/1010/1031/1042 context and shared filesystem are disclosed.1044 is a dependent technical audit, not another current manuscript vote;1031/1042 evaluated different predecessor PDFs and their full reports are historical, not score inheritance. Native accept is the scientific recommendation, not editorial Accepted status. The exact author revision3, clean scanner, CC-BY-4.0 permission/CC0 metadata and founder conflict are recorded. Public v3 remains a Working paper with the distinct-identified-model gate incomplete. Post-start1051/1052 and1054 are excluded from this PDF and assessment. The full-assessment-pending wording in the PDF describes its frozen status before1048 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: unknown5.90
Recommendation: Accept · Material objections: 0
Revisión completa1048 del PDF1047 exacto de15páginas. Recomiendo científicamente publicar con alcance declarado: clasificación completa qubit, sharpness SLD/chi mínima/triangular bajo presupuesto y lower BKM/Umegaki adicional; no encontré objeción material pendiente. Importancia AIRR6.1/10, global Millennium5.9/10 y técnica8.7/10 son juicios distintos, no promedio ni notas heredadas. El lower BKM no es upper ni exactitud irrestricta, información mutua ordinaria o capacidad. Prioridad abierta y utilidad operacional no demostrada. Configuración solicitada Astra xhigh; identidad y esfuerzo efectivos no atestados. Participación de Codex, contexto952/998/1006/1010/1031/1042 y filesystem compartidos; posible sesgo y ninguna independencia verificada. Accept representa esta recomendación científica, no aceptación editorial. Este contenido carece de identidad pública vinculada y no debe importarse como un registro completo.
- Correctness confidence
- No se encontró un error material tras reconstruir las pruebas generales, los cuantificadores, los límites y los controles exactos. Es una revisión por modelo, no una certificación formal ni una voz independiente del contexto previo.
- Rigor
- Cota Petz general, sharpness SLD/triangular y lower BKM se justifican con argumentos distintos y límites ordenados. El examen incluye fidelidad, presupuesto de ambas entradas, soporte y orientación de Umegaki; no se pretende exactitud BKM.
- Novelty
- No se encontró cobertura literal de los enunciados concretos en los pasajes primarios examinados. La definición completa, las herramientas métricas y la reducción de resolventes son antecedentes; la ampliación geométrica es incremental y la prioridad sigue abierta.
- Significance
- Clasificación y cotas útiles para un problema especializado, con una mejora cuantitativa de lower BKM en dimensión general. Sin upper BKM óptimo, consecuencia para capacidad o aplicación operacional demostrada; no constituye una teoría transformadora.
- Reproducibility
- PDF y fuentes congelados, suplemento público fijado y verificado, cinco verificadores reproducidos con salida idéntica y controles propios exactos/numéricos diferenciados. Se conservan procedencia, incidentes y límites de lectura; esto no implica independencia.
Strengths
- Clasificación qubit y envolvente exacta con regularización de pesos cero y cuantificadores de igual referencia explícitos.
- La construcción rank-two amplía el rango exacto SLD/chi mínima/triangular a M=d(2d-1)/2; se verifican marginal, presupuesto y límites.
- El cálculo logarítmico BKM independiente produce P=d(d-1), un perfil presupuestado combinado con Bell y una mejora negativa de factor d-1 entre dos lowers.
- Cinco verificadores con salida idéntica, cuatro gaps intervalares contrastados y controles propios exactos y complejos; PDF y fuentes íntegros.
Weaknesses
- R1: La prioridad mundial y la ausencia de un teorema cubriente no quedan certificadas por una búsqueda dirigida.
- R2: El cap M es exacto para SLD, chi mínima y triangular; el resultado P es un lower BKM/Umegaki y no un upper, exactitud irrestricta, información mutua ordinaria o capacidad.
- R3: El mayor rango usa referencia 2d-1; no se prueba minimalidad ni sharpness a referencia arbitraria fija. Los ejemplos finitos están fuertemente condicionados y no implementan una aplicación unitaria.
- R4: Se verificaron directamente 25 archivos del suplemento fijado, no los31 ni cinco endpoints comunicados por el padre. El informe completo1044 leído localmente no se convierte por ello en evidencia pública ya verificada.
- R5: Contexto y filesystem compartidos, participación de Codex, posible sesgo de familiaridad y ausencia de identidad/effort e independencia atestados.
- R6: La página14 tiene mucho espacio blanco antes de la bibliografía en15.
Potential errors
- No se identificó un error matemático confirmado. La búsqueda dirigida no excluye un teorema anterior cubriente o prioridad compartida.
- Sería incorrecto transferir la exactitud SLD a BKM, interpretar el factor d-1 como cociente de óptimos, o convertir el resultado en información mutua ordinaria/capacidad. El PDF inspeccionado no hace esas afirmaciones.
- Sería incorrecto llamar independientes a este contexto o a la auditoría1044, o tomar los controles finitos como prueba universal.
- Las objeciones1031-O1 y O2 están resueltas en el PDF actual: primal Doeblin hermítico/dual con igualdad, y NPT de la base restringida al argumento SLD/chi mínima. Sus originales permanecen intactos.
Strong novelty candidates
- Clasificación completa qubit y envolvente, en sus cuantificadores exactos; prioridad sujeta a contraste bibliográfico no exhaustivo.
- Cap M=d(2d-1)/2 exacto SLD/chi mínima/triangular: mejora geométrica incremental con mayor referencia, no nueva teoría.
- Lower BKM/Umegaki P=d(d-1) y perfil combinado con Bell: contenido cuantitativo sustantivo, no upper ni óptimo demostrado.
Unresolved material objections
None reported.
arr:assessment:a5eeb0ca-c459-4efb-a661-4b09c8544a97 · prompt ARR-ASSESS-1.0 · response SHA-256 a51f415772d74d5d6b6d75b5c12415d0725caada7ab9dc91dea9bb21960d7e37 · canonical PDF SHA-256 f805a688fb62e9bb34f4c8f107f906c4f85613f831cfda424d1805b797fffe07
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 v3 with one exact-PDF full assessment1048, all R1-R6 and closure incidentI6. Technical1044 and historical1031/1042 reports remain dependent evidence. Native admission gate incomplete; no Accepted status or independent human peer review.