Dimension bounds for common components after measurable quantum preparation
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
For a channel on a d-dimensional system with ordinary trace-distance contraction at most r, we give a common-component certificate after an explicitly specified measurable preparation instrument. Its mass is at least max{0, 1-(d-1)r}, independently of the outcome cardinality. The same certificate yields a completely positive replacement component after the associated measure-and-prepare channel. We determine the worst-case envelope of this positive component over the stated class using classical exclusion channels. We separate these assertions from optimal complete contraction and from mixing of arbitrary observed instruments. Two elementary examples show why the recorded instrument and the topology on posterior laws must be retained. The measurement coefficient, replacement framework, and downstream contraction principles are established prior results; worldwide novelty of the dimension comparison is not asserted.
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Cite this paper
Lluis Eriksson (2026). Dimension bounds for common components after measurable quantum preparation. AIRR.SCIENCE, ARR-2026-1PBZ1Q7T588FW9M1, v1. https://airr.science/notes/ARR-2026-1PBZ1Q7T588FW9M1/versions/v1/ Technical note; ARR-2026-1PBZ1Q7T588FW9M1 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 Not peer reviewed by AIRR.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.
Technical-note scope
- Kind
- Result
- Maturity
- Complete In Scope
Contribution boundary
Dimension-dependent positive common-component certificate after a measurable preparation instrument, with a sharp worst-case positive-component envelope.
Limitations
Preparation structure and reference/output restrictions retained. Modest elementary contribution; worldwide novelty unresolved. No arbitrary-instrument mixing theorem or optimal complete entropy coefficient claimed.
AI assistance statement
The author directed substantial OpenAI Codex assistance in derivation, writing and numerical work. One full exact-PDF review requested GPT-6 Astra xhigh in a separate context; effective runtime identity, effort, isolation and independence are unattested, shared filesystem and parent authoring involvement disclosed. Overall3.5, technical8.5, importance3.0; minor revision, no material mathematical error found. Full original report and all nonblocking objections O1-O4 preserved. This is one judgment, not verified independent human review or editorial acceptance. The PDF pending-review statement predates this completed assessment. Worldwide novelty is unresolved.
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
- 3.50–3.50
- 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; Benchmark match incomplete; Adverse reports or unresolved objections require editorial disposition
Review input clarification
One full exact-PDF REVIEW1211 judgment: overall3.5, technical8.5, importance3.0; minor revision, no material mathematical error found. Operator projection serializes that same judgment, not a second evaluation. Full original report, verdict, selected-source scope and nonblocking O1-O4 are linked below. Requested GPT-6 Astra xhigh in a separate context; effective runtime identity, effort, isolation and independence unattested. Shared filesystem, parent Codex authoring involvement and visible prior unscored-audit summary disclosed. O1 attribution precision; O2 optional N-1 cardinality refinement; O3 checker coverage/navigation and retained raw newline mismatch; O4 novelty unresolved. PDF pending-assessment text describes freeze-time status. Case SUB-D762F2FF53E5DC53, scanner clean; native exact CC BY4/CC0 permission recorded2026-10-29T03:58:18Z. Author/operator conflict disclosed. Working paper, not editorial admission, independent human review or certified worldwide priority.
Operator record · · Source files and affected reports
- REVIEW1211.txt · SHA-256
ac9794b0e35217253234874d6d1541d077ce9a1ad1406d1d973d0ce6ee1f81be - verdict1211.json · SHA-256
55d3a33e2a9ae746633a72e3ab6d48b9ae37f31ef967a9cc8af339c1b0c45e12 - review-context.txt · SHA-256
2e4bd807fda1cb54c1660e6d2e00d68c37e41a55dcafd55a6889871e26b4df1d - readings1211.json · SHA-256
60e4f6d38d04db4a866ad7767a8261ddea448c7a7553cdece5b7ea0ad3852c7a - projection-provenance.json · SHA-256
c7dfe0280398539dc685eb23882e657c20ce8dd4353e9889258f6500e2e97d3b
OpenAI (requested; runtime unverified) · GPT-6 Astra xhigh (requested; runtime unverified) · unknown · review context: unknown3.50
Recommendation: Minor Revision · Material objections: 0
Operator serialization of the single original REVIEW1211 judgment for this exact PDF. No material mathematical error found; minor revision. A correct sharp but modest spectral certificate built from prior common-component machinery. Worldwide novelty unresolved. Requested GPT-6 Astra xhigh; effective identity, effort and independence unattested; shared filesystem and parent involvement disclosed. Overall3.5; separate technical8.5 and importance3.0. Full original report, verdict and O1-O4 are preserved with this record; this mapping is not a second evaluation.
- Correctness confidence
- All principal proofs checked, no in-scope counterexample found; fallible inspection, not formal certification.
- Rigor
- Self-contained arguments handle integrability, positivity, endpoints and reference/output boundaries; attribution and finite-count comparison can be sharpened.
- Novelty
- Specific dimension comparison not located in selected readings; ingredients and measurable minorization are prior. Worldwide originality is unverified.
- Significance
- Useful outcome-independent certificate and sharp universal obstruction, but narrow scope and no developed new application or limit theorem.
- Reproducibility
- Full self-contained manuscript and finite checks are inspectable; replay is semantically successful. Public supplement navigation was not verified, and finite checks are not a general proof certificate.
Strengths
- Self-contained spectral and Choi arguments with endpoint and measurability boundaries.
- Sharp positive-component envelope with an elementary exclusion-channel witness.
Weaknesses
- Make prior general-outcome minorization and the positive-component divergence attribution more explicit. Existing broad attribution is not false.
- N is a valid cited sufficient constant, but the elementary finite-outcome improvement N-1 is available.
- The broad pinned repository pointer could give exact supplement paths and replay commands. Original 1206 labels exceed direct branch-count and iteration coverage.
- Worldwide priority of the dimension envelope is unverified. Core ingredients and measurable minorization are established, limiting demonstrated novelty and significance.
Potential errors
None reported.
Strong novelty candidates
- Specific sharp dimension comparison not found in selected readings; worldwide originality unverified.
Unresolved material objections
None reported.
arr:assessment:f327de6a-5915-496c-9043-eb9b2c576d4a · prompt ARR-ASSESS-1.0 · response SHA-256 13e97993fcf1476d2a90e01e4265a57a53208dd7165ff476f5a1a42c6bc91905 · canonical PDF SHA-256 65b320e9a3277ce6565ec3496acf3466f1d59313c1c3aafc016f573eec08bd71
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Author-authorized citable Working paper, not admitted to the AIRR accepted collection. Operator/author conflict disclosed. No independent human decision or native acceptance gate completion claimed.