{"paper":{"title":"Quantum entanglement, sum of squares, and the log rank conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"Boaz Barak, David Steurer, Pravesh Kothari","submitted_at":"2017-01-23T10:25:42Z","abstract_excerpt":"For every $\\epsilon>0$, we give an $\\exp(\\tilde{O}(\\sqrt{n}/\\epsilon^2))$-time algorithm for the $1$ vs $1-\\epsilon$ \\emph{Best Separable State (BSS)} problem of distinguishing, given an $n^2\\times n^2$ matrix $\\mathcal{M}$ corresponding to a quantum measurement, between the case that there is a separable (i.e., non-entangled) state $\\rho$ that $\\mathcal{M}$ accepts with probability $1$, and the case that every separable state is accepted with probability at most $1-\\epsilon$. Equivalently, our algorithm takes the description of a subspace $\\mathcal{W} \\subseteq \\mathbb{F}^{n^2}$ (where $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06321","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"}