{"paper":{"title":"Dvoretzky's Theorem and the Complexity of Entanglement Detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"quant-ph","authors_text":"Guillaume Aubrun, Stanislaw Szarek","submitted_at":"2015-10-02T12:38:59Z","abstract_excerpt":"The well-known Horodecki criterion asserts that a state $\\rho$ on $\\mathbf{C}^d \\otimes \\mathbf{C}^d$ is entangled if and only if there exists a positive map $\\Phi : \\mathsf{M}_d \\to \\mathsf{M}_d$ such that the operator $(\\Phi \\otimes \\mathrm{Id})(\\rho)$ is not positive semi-definite. We show that the number of such maps needed to detect all the robustly entangled states (i.e., states $\\rho$ which remain entangled even in the presence of substantial randomizing noise) exceeds $\\exp(c d^3 / \\log d)$. The proof is based on the 1977 inequality of Figiel--Lindenstrauss--Milman, which ultimately re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00578","kind":"arxiv","version":3},"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"}