{"paper":{"title":"Three-qutrit entanglement and simple singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"quant-ph","authors_text":"Fr\\'ed\\'eric Holweck, Hamza Jaffali","submitted_at":"2016-06-17T14:41:40Z","abstract_excerpt":"In this paper, we use singularity theory to study the entanglement nature of pure three-qutrit systems. We first consider the algebraic variety $X$ of separable three-qutrit states within the projective Hilbert space $\\mathbb{P}(\\mathcal{H}) = \\mathbb{P}^{26}$. Given a quantum pure state $|\\varphi\\rangle\\in \\mathbb{P}(\\mathcal{H})$ we define the $X_\\varphi$-hypersuface by cutting $X$ with a hyperplane $H_\\varphi$ defined by the linear form $\\langle\\varphi|$ (the $X_\\varphi$-hypersurface of $X$ is $X\\cap H_\\varphi \\subset X$).\n  We prove that when $|\\varphi\\rangle$ ranges over the SLOCC entangl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05537","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"}