Bell and tripartite anchor sectors for finite-copy Werner witnesses
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We establish strictly positive sectors of the Werner endpoint partial-trace form on rank-at-most-two coefficient matrices. A support plane must contain one specified vector, assembled from Bell vectors on pairs of original slots and GHZ vectors on triples of qutrit slots; the second vector and both coefficient covectors remain unrestricted. For a Bell pair we prove the required signed co-Choi comparison in every local dimension at least three, using a polynomial identity in a 24-diagram algebra with the dimension as a parameter. A separate rational certificate covers a genuinely tripartite three-qutrit GHZ block. Exact kernels and uniform nonunit spectral intervals give an explicit strict lower bound under any finite combination of these blocks, including a qutrit sector for every copy count at least two. A perturbation bound includes the actual dimension-dependent norm factor. The Schur and signed tensor-contraction mechanism is attributed to Wu and Zou; the added inputs are the two block comparisons and their quantitative kernels. The proof is computer assisted, with exact rational arithmetic and symbolic identities, not numerical spectral extrapolation. The support restriction remains substantive and no unrestricted finite-copy positivity or NPT bound-entanglement result follows.
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Cite this paper
Lluis Eriksson (2026). Bell and tripartite anchor sectors for finite-copy Werner witnesses. AIRR.SCIENCE, ARR-2026-16NB5DD5M18TTBET, v1. https://airr.science/papers/ARR-2026-16NB5DD5M18TTBET/versions/v1/ Research preprint; ARR-2026-16NB5DD5M18TTBET v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.
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- C1 · resolved · page2 Corollary2; TeX62-64: Explicit min-phase Euclidean distance agrees with unchanged continuity proof; constants unchanged.
- C2 · resolved · page2 section1.1; TeX77: Completed bounded Bell/GHZ comparison with explicit limits; compatible with own390primary-source reading, no universal priority claim.
- C3 · resolved · page7 section6 and page8 reference6; TeX300,341-345: CGL1999Eq1codewords and erasure/single-share properties explicitly credited; product-code exclusion distinguished from general quantum-code membership.
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