{"paper":{"title":"Dimension formula for induced maximal faces of separable states and genuine entanglement","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":"2015-01-05T02:00:24Z","abstract_excerpt":"The normalized separable states of a finite-dimensional multipartite quantum system, represented by its Hilbert space ${\\cal H}$, form a closed convex set ${\\cal S}_1$. The set ${\\cal S}_1$ has two kinds of faces, induced and non-induced. An induced face, $F$, has the form $F=\\Gamma(F_V)$, where $V$ is a subspace of ${\\cal H}$, $F_V$ is the set of $\\rho\\in{\\cal S}_1$ whose range is contained in $V$, and $\\Gamma$ is a partial transposition operator. Such $F$ is a maximal face if and only if $V$ is a hyperplane. We give a simple formula for the dimension of any induced maximal face. We also prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00745","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"}