Metadata
bibkey: gnp2025dickeextensions
authors: Aabhas Gulati, Ion Nechita and Sang-Jun Park
year: 2025
title: Positive maps and extendibility hierarchies from copositive matrices
doi: 10.48550/arXiv.2509.15201
claim: arXiv:2509.15201v4 Question 8.20 asks whether the fully PPT Bose symmetric complete graph and star extension cones agree for mixtures of Dicke states.
strata_touched:
- D5/S3/Quantum/Entanglement/SymmetricExtensions/DickeExtension
license: citation-only
triage: anchor
Positive maps and extendibility hierarchies from copositive matrices
Verified locator
DOI: https://doi.org/10.48550/arXiv.2509.15201.
The versioned source is arXiv:2509.15201v4, Question 8.20. Its literal question reads:
For mixtures of Dicke states, are the following two sets equivalent?
The operator coordinates are the nonnegative coefficients of the orthonormal two-particle Dicke vectors. The star uses one root and r-1 interchangeable leaves; the complete graph uses all r registers symmetrically. Marginals are unnormalized partial traces and PPT means positivity under every register cut. The formal statement retains the whole nonnegative cone, including zero.
The current journal identifier is DOI 10.1007/s00023-026-01763-3. Its subscription preview supplied no acquired question-body text. The journal question wording remains unverified. The versioned arXiv question does not establish current-source resolution, priority or absence of a published solution.
The defining source passages are Section 2’s Dicke cone, Definition 8.1’s root-times-symmetric-leaves extension and Section 8.2’s globally Bose symmetric complete-graph extension. The sentence preceding Question 8.20 explicitly leaves this equality unknown. The exact target excludes the broader comparison for arbitrary Bose marginals and Question 8.7.
The supplied bounded source evidence for the preregistered event comprises the original-PDF readings of arXiv:2309.16655v2, arXiv:2001.04440v1 and arXiv:1706.09423v2, a nine-record INSPIRE citation screen, and HAL, author and accepted-source checks. No full resolution of this exact event was found in that checked scope. The inspected Section 6 passage of Britz-Laurent, arXiv:2512.06551v2 cites the Dicke question while discussing a broader Bose comparison; this is not independent proof that the Dicke subcase remains open. arXiv:2602.15800v2, Section 5.2, including Lemma 5.8 and Theorem 5.9, starts from full global Bose extensions. Its full-projector premise does not supply the star-to-complete implication. These are bounded negative findings, not an exhaustive novelty or priority certificate. The journal question-body characters acquired from the subscription preview are zero; no journal question or journal solution status is asserted.
The repository’s application is described in the canonical Blueprint and the versioned question dossier. The elementary support argument is repo-derived from existing frozen results; the definitions and question above are literature-attested. This distinction makes no worldwide originality claim.