{"paper":{"title":"Existence of locally maximally entangled quantum states via geometric invariant theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.RT","quant-ph"],"primary_cat":"math.AG","authors_text":"Jim Bryan, Mark Van Raamsdonk, Zinovy Reichstein","submitted_at":"2017-08-04T19:17:20Z","abstract_excerpt":"We study a question which has natural interpretations in both quantum mechanics and in geometry. Let $V_1,..., V_n$ be complex vector spaces of dimension $d_1,...,d_n$ and let $G= SL_{d_1} \\times \\dots \\times SL_{d_n}$. Geometrically, we ask given $(d_1,...,d_n)$, when is the geometric invariant theory quotient $\\mathbb{P}(V_1 \\otimes \\dots \\otimes V_n)// G$ non-empty? This is equivalent to the quantum mechanical question of whether the multipart quantum system with Hilbert space $V_1\\otimes \\dots \\otimes V_n$ has a locally maximally entangled state, i.e. a state such that the density matrix f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01645","kind":"arxiv","version":2},"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"}