{"paper":{"title":"Boundary of the set of separable states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dragomir Z. Djokovic, Lin Chen","submitted_at":"2014-04-03T00:02:01Z","abstract_excerpt":"Motivated by the separability problem in quantum systems $2\\otimes4$, $3\\otimes3$ and $2\\otimes2\\otimes2$, we study the maximal (proper) faces of the convex body, $S_1$, of normalized separable states in an arbitrary quantum system with finite-dimensional Hilbert space $H=H_1\\otimes H_2\\otimes\\cdots\\otimes H_n$. To any subspace $V$ of $H$ we associate a face $F_V$ of $S_1$ consisting of all states $\\rho\\in S_1$ whose range is contained in $V$. We prove that $F_V$ is a maximal face if and only if $V$ is a hyperplane. If $V$ is the hyperplane orthogonal to a product vector, we prove that $\\dim F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0738","kind":"arxiv","version":4},"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"}