{"paper":{"title":"A gap for PPT entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Daniel Cariello","submitted_at":"2016-09-22T17:26:18Z","abstract_excerpt":"Let $W$ be a finite dimensional vector space over a field with characteristic not equal to 2. Denote by $\\text{Sym}(V)$ and $\\text{Skew-Sym}(V)$ the subspaces of symmetric and skew-symmetric tensors of a subspace $V$ of $W\\otimes W$, respectively. In this paper we show that if $V$ is generated by tensors with tensor rank 1, $V=\\text{Sym}(V)\\oplus\\text{Skew-Sym}(V)$ and $W$ is the smallest vector space such that $V\\subset W\\otimes W$ then $\\dim(\\text{Sym}(V))\\geq\\max\\{\\frac{2\\dim(\\text{Skew-Sym}(V))}{\\dim(W)}, \\frac{\\dim(W)}{2}\\}$.\n  This result has a straightforward application to the separabi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07079","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}