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 Not peer reviewed.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 earlier ladder lower is not a unitary phase model. Faithful limits, prior dependencies, adverse controls and review-context limits are explicit. A separate norm-one local Hamiltonian with reference dimension d realizes the BKM/Umegaki lower at fixed finite phase. Certified relative-entropy pairs exceed the common-Bell-diagonal class at both noise signs. The exact classical benchmark is reconstructed throughout the physical noise range, without a classical priority claim. The phase family spends order approaching d squared and loses absolute information in its limiting construction. An explicit dimension-scaled family gives a linearly growing relative Bell separation with vanishing information and polynomial-in-dimension conditioning. A joint binary measurement retains its leading output relative entropy. No fixed-noise operational advantage, resource optimum or unrestricted coefficient is claimed.
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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, v4. https://airr.science/papers/ARR-2026-77DGRYDGXD8MDSY2/versions/v4/ Research preprint; ARR-2026-77DGRYDGXD8MDSY2 v4. 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. Adds finite-phase relative-entropy realizations, full-noise classical benchmark with prior limits, fixed-parameter dimension-scaled resource laws and an explicit joint binary measurement. Full exact23-page review1084 and all O1-O6 accompany the new PDF; earlier versions and their reports remain immutable.
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 review1084 examined this exact23-page PDF1083, SHA256 255ca15a68df24944e2f3623265e9912ca7cad1d75e96074fadb304c0f83eb7e. Scientific importance6.3/10, global Millennium6.1/10 and technical quality8.7/10 are distinct judgments, not an average. The catalogue global6.1 is not technical8.7. The full report recommends scientific publication with declared scope and no confirmed unresolved material objection. All O1-O6 and I1-I7 remain visible. Priority and precise Lee-Makur full-text coverage are open. Dimension-dependent noise, vanishing absolute information, conditioning, rare events, quantum input denominator and lack of a general BKM/Umegaki upper, capacity or robust fixed-noise operational advantage limit the results. Requested GPT-6 Astra xhigh; effective model identity, effort, isolation and independence are unattested. Substantial OpenAI Codex derivation/writing/numerical work, reused952/1048 context and shared filesystem are disclosed. Five replays are not five reviewers.1044/1054/1058/1068/1077 are dependent component audits;1031/1042/1048 concern predecessor PDFs. None is an additional current vote or inherited grade. The exact linked author revision4, clean scanner, CC BY4.0 permission/CC0 metadata and founder conflict are recorded. Working paper only, not Accepted or independently human-reviewed; the native two-distinct-identified-model admission gate is incomplete. The full-assessment-pending wording in the frozen PDF describes its status before1084 completed. Exploratory1075/1081 are excluded.
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
- 6.10–6.10
- 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 review1084 examined this exact23-page PDF1083, SHA256 255ca15a68df24944e2f3623265e9912ca7cad1d75e96074fadb304c0f83eb7e. Scientific importance6.3/10, global Millennium6.1/10 and technical quality8.7/10 are distinct judgments, not an average. The catalogue global6.1 is not technical8.7. The full report recommends scientific publication with declared scope and no confirmed unresolved material objection. All O1-O6 and I1-I7 remain visible. Priority and precise Lee-Makur full-text coverage are open. Dimension-dependent noise, vanishing absolute information, conditioning, rare events, quantum input denominator and lack of a general BKM/Umegaki upper, capacity or robust fixed-noise operational advantage limit the results. Requested GPT-6 Astra xhigh; effective model identity, effort, isolation and independence are unattested. Substantial OpenAI Codex derivation/writing/numerical work, reused952/1048 context and shared filesystem are disclosed. Five replays are not five reviewers.1044/1054/1058/1068/1077 are dependent component audits;1031/1042/1048 concern predecessor PDFs. None is an additional current vote or inherited grade. The exact linked author revision4, clean scanner, CC BY4.0 permission/CC0 metadata and founder conflict are recorded. Working paper only, not Accepted or independently human-reviewed; the native two-distinct-identified-model admission gate is incomplete. The full-assessment-pending wording in the frozen PDF describes its status before1084 completed. Exploratory1075/1081 are excluded.
Operator record · · Source files and affected reports
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OpenAI · effective-model-unattested; requested GPT-6 Astra xhigh · involved in manuscript · review context: unknown6.10
Recommendation: Accept · Material objections: 0
Revisión completa1084 del PDF1083 exacto de23p, SHA256 255ca15a68df24944e2f3623265e9912ca7cad1d75e96074fadb304c0f83eb7e. No se confirmó objeción matemática material tras lectura completa, reconstrucción analítica y controles acotados. Recomiendo publicación científica con alcance declarado; accept no significa aceptación editorial. Clasificación exacta qubit, perfiles de orden y familias explícitas de fase/medición aportan resultados especializados; herramientas y preparaciones son previas, prioridad abierta. ImportanciaAIRR6.3, globalMillennium6.1 y técnica8.7 son juicios separados, no promedios ni probabilidades. Contexto952/1048 y antecedentes reutilizados, filesystem compartido y participaciónCodex declarada; identidad/effort efectivos e independencia no atestados. No se heredan notas. LímitesO1–O6 y adversos íntegros en informe/veredicto. No IDs públicos suministrados: contenido sin vinculación nativa y sin relación con1005v1.
- Correctness confidence
- Reconstrucción de pruebas generales, geometría ambiental y límites; cinco replays coincidentes y controles propios. No hay error material confirmado, pero no es verificación formal ni humana independiente.
- Rigor
- Distingue supremum/realización finita, SLD/triangular/all-Petz/BKM, orden del marginal real y límites ordenados. Los óptimos abiertos no se prometen como resultados.
- Novelty
- Candidatas: clasificación exacta y rangos/constantes de familias explícitas. Definiciones, preparaciones, maquinaria clásica y metrología son previas. Lee–Makur completo no leído; búsqueda dirigida, no exhaustiva.
- Significance
- Contribución especializada relevante con una separación medida explícita. No determina BKM/Umegaki generales, una frontera de recursos, capacidad ni ventaja experimental a ruido fijo.
- Reproducibility
- PDF/fuentes congelados, informes y adversos conservados, cinco reproducciones idénticas, controles exactos e intervalos. No se reprodujo toda la campaña ni se certifica independencia de bibliotecas o revisores.
Strengths
- Clasificación completa SLD/chi_min/triangular de canales unitales qubit con normalizaciónChoi y regularizaciones correctas.
- Rangos separados Bell d²/2 all-Petz, rango dos M=d(2d−1)/2 SLD/triangular y lowerBKM/Umegaki P=d(d−1), con presupuesto del marginal real.
- Familia de fase local finita con identidades exactas, separación comúnBell para ambos signos y costes cuantificados.
- Escalado a parámetros fijos y proyector binario ambiental explícito que conserva la información de salida principal; falsadores a extensiones preservados.
- Pruebas legibles, seis certificados finitos reproducidos con intervalos, cinco replays coincidentes y controles propios con geometría ambiental.
Weaknesses
- O1: Herramientas, definición completa y preparaciones son previas; falta la fórmula/prueba íntegra de Lee–Makur. Una búsqueda vacía no acredita novedad.
- O2: Ruido dependiente de dimensión, denominador cuántico e información absoluta decreciente; no capacidad, MI ordinaria, óptimo, ventaja experimental ni canal clásico binario nuevo.
- O3: Tras el benchmark all-Petz convendría repetir Umegaki/triangular al invocar la familia de fase; los enunciados completos delimitan la clase y no se confirma error.
- O4: Contexto compartido y bibliotecas dependientes; replays no son revisores independientes. No se revalidaron todos los archivos remotos ni programas históricos.
- O5: Abstract largo, abundantes identificadores internos y carga histórica. No impide reconstruir pruebas, pero dificulta la lectura científica continua.
- O6: t fijo no puede reemplazarse por t_d; vector límite constante y orientación inversa pierden información; tolerancia angular sólo suficiente dentro del plano.
Potential errors
- No se confirmó un error material en el PDF1083; esto no certifica inexistencia de errores.
- Un teorema primario no identificado puede cubrir parte de la contribución; cobertura precisa Lee–Makur no comprobada.
- No transferir exactitudSLD/triangular al BKM/Umegaki general ni al conjunto all-Petz de rango mayor.
- No extrapolar el modelo especial de fase a todas las órbitas unitarias, ni intercambiar límites o medir la entrada manteniendo el denominador cuántico.
- La reproducción acotada comparte código e historia; no acredita aislamiento, independencia ni toda la campaña o publicación remota.
Strong novelty candidates
- Candidata condicionada a prioridad: fórmula completa de canales unitales qubit y envolvente exacta.
- Candidatos condicionados a prioridad: rango principal de orden y constante logarítmica P con cuantificadores separados.
- Candidata constructiva: realización finita de fase, constantes de costes a parámetros fijos y proyector simplificado con probabilidades exactas que conserva el leading output. Preparación, asistencia por ancilla y teoría de entropía medida son previas.
Unresolved material objections
None reported.
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A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Full review1084 examined this exact23-page PDF1083, SHA256 255ca15a68df24944e2f3623265e9912ca7cad1d75e96074fadb304c0f83eb7e. Scientific importance6.3/10, global Millennium6.1/10 and technical quality8.7/10 are distinct judgments, not an average. The catalogue global6.1 is not technical8.7. The full report recommends scientific publication with declared scope and no confirmed unresolved material objection. All O1-O6 and I1-I7 remain visible. Priority and precise Lee-Makur full-text coverage are open. Dimension-dependent noise, vanishing absolute information, conditioning, rare events, quantum input denominator and lack of a general BKM/Umegaki upper, capacity or robust fixed-noise operational advantage limit the results. Requested GPT-6 Astra xhigh; effective model identity, effort, isolation and independence are unattested. Substantial OpenAI Codex derivation/writing/numerical work, reused952/1048 context and shared filesystem are disclosed. Five replays are not five reviewers.1044/1054/1058/1068/1077 are dependent component audits;1031/1042/1048 concern predecessor PDFs. None is an additional current vote or inherited grade. The exact linked author revision4, clean scanner, CC BY4.0 permission/CC0 metadata and founder conflict are recorded. Working paper only, not Accepted or independently human-reviewed; the native two-distinct-identified-model admission gate is incomplete. The full-assessment-pending wording in the frozen PDF describes its status before1084 completed. Exploratory1075/1081 are excluded.