{"paper":{"title":"Entanglement thresholds for random induced states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"quant-ph","authors_text":"Deping Ye, Guillaume Aubrun, Stanislaw J. Szarek","submitted_at":"2011-06-11T22:41:51Z","abstract_excerpt":"For a random quantum state on $H=C^d \\otimes C^d$ obtained by partial tracing a random pure state on $H \\otimes C^s$, we consider the whether it is typically separable or typically entangled. For this problem, we show the existence of a sharp threshold $s_0=s_0(d)$ of order roughly $d^3$. More precisely, for any $a > 0$ and for d large enough, such a random state is entangled with very large probability when $s < (1-a)s_0$, and separable with very large probability when $s > (1+a)s_0$. One consequence of this result is as follows: for a system of N identical particles in a random pure state, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2264","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"}