{"paper":{"title":"Extremal entanglement witnesses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"(2) Department of Physics, Andreas Hauge (1), Jan Myrheim (1), Leif Ove Hansen (1), Norwegian University of Science, Per {\\O}yvind Sollid (2) ((1) Department of Physics, Technology, University of Oslo)","submitted_at":"2013-05-10T16:44:33Z","abstract_excerpt":"We study extremal entanglement witnesses on a bipartite quantum system. We define the cone of witnesses as the dual of the set of separable density matrices, thus $\\textrm{Tr}\\,\\Omega\\rho\\geq 0$ when $\\Omega$ is a witness and $\\rho$ a pure product state, $\\rho=\\psi\\psi^{\\dagger}$ with $\\psi=\\phi\\otimes\\chi$. The set of witnesses of unit trace is a compact convex set, defined by its extremal points. The expectation value $f(\\phi,\\chi)=\\mathrm{Tr}\\,\\Omega\\rho$ as a function of $\\phi$ and $\\chi$ is a nonnegative biquadratic form. Every zero of $f(\\phi,\\chi)$ imposes real-linear constraints on $f$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2385","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"}