{"paper":{"title":"Separability criteria with angular and Hilbert space averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C.H. Oh, Kazuo Fujikawa, Koichiro Umetsu, Sixia Yu","submitted_at":"2016-03-06T06:15:33Z","abstract_excerpt":"The practically useful criteria of separable states $\\rho=\\sum_{k}w_{k}\\rho_{k}$ in $d=2\\times2$ are discussed. The equality $G({\\bf a},{\\bf b})= 4[\\langle \\psi|P({\\bf a})\\otimes P({\\bf b})|\\psi\\rangle-\\langle \\psi|P({\\bf a})\\otimes{\\bf 1}|\\psi\\rangle\\langle \\psi|{\\bf 1}\\otimes P({\\bf b})|\\psi\\rangle]=0$ for any two projection operators $P({\\bf a})$ and $P({\\bf b})$ provides a necessary and sufficient separability criterion in the case of a separable pure state $\\rho=|\\psi\\rangle\\langle\\psi|$. We propose the separability criteria of mixed states, which are given by ${\\rm Tr}\\rho\\{{\\bf a}\\cdot "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01792","kind":"arxiv","version":1},"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"}