{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HOIEI42Q2HONNLB2NNJS3NACX6","short_pith_number":"pith:HOIEI42Q","schema_version":"1.0","canonical_sha256":"3b90447350d1dcd6ac3a6b532db402bfae9eb797d780732c36bf792dda3ff93a","source":{"kind":"arxiv","id":"1106.2264","version":3},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.2264","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-11T22:41:51Z","cross_cats_sorted":["math.FA","math.PR"],"title_canon_sha256":"2f0b51d7601e95ebb4d39611aae8252b2d693033888f2b9dc629bdbf18e0d9f0","abstract_canon_sha256":"910dea900f3970b71766b1c04a2c97a5841beda9ef0ea393f330ef1fae7e2e50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:21.798043Z","signature_b64":"NXQ2/UgHBYO6XMjTMBJhRJvYFlRKsT1W4gwlKC15dhekgU1WhtZlJd//8SY39R7b/F7YBK9cuyDu/7uEBFZZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b90447350d1dcd6ac3a6b532db402bfae9eb797d780732c36bf792dda3ff93a","last_reissued_at":"2026-05-18T02:16:21.797274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:21.797274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.2264","created_at":"2026-05-18T02:16:21.797418+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.2264v3","created_at":"2026-05-18T02:16:21.797418+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2264","created_at":"2026-05-18T02:16:21.797418+00:00"},{"alias_kind":"pith_short_12","alias_value":"HOIEI42Q2HON","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HOIEI42Q2HONNLB2","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HOIEI42Q","created_at":"2026-05-18T12:26:30.835961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HOIEI42Q2HONNLB2NNJS3NACX6","json":"https://pith.science/pith/HOIEI42Q2HONNLB2NNJS3NACX6.json","graph_json":"https://pith.science/api/pith-number/HOIEI42Q2HONNLB2NNJS3NACX6/graph.json","events_json":"https://pith.science/api/pith-number/HOIEI42Q2HONNLB2NNJS3NACX6/events.json","paper":"https://pith.science/paper/HOIEI42Q"},"agent_actions":{"view_html":"https://pith.science/pith/HOIEI42Q2HONNLB2NNJS3NACX6","download_json":"https://pith.science/pith/HOIEI42Q2HONNLB2NNJS3NACX6.json","view_paper":"https://pith.science/paper/HOIEI42Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.2264&json=true","fetch_graph":"https://pith.science/api/pith-number/HOIEI42Q2HONNLB2NNJS3NACX6/graph.json","fetch_events":"https://pith.science/api/pith-number/HOIEI42Q2HONNLB2NNJS3NACX6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HOIEI42Q2HONNLB2NNJS3NACX6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HOIEI42Q2HONNLB2NNJS3NACX6/action/storage_attestation","attest_author":"https://pith.science/pith/HOIEI42Q2HONNLB2NNJS3NACX6/action/author_attestation","sign_citation":"https://pith.science/pith/HOIEI42Q2HONNLB2NNJS3NACX6/action/citation_signature","submit_replication":"https://pith.science/pith/HOIEI42Q2HONNLB2NNJS3NACX6/action/replication_record"}},"created_at":"2026-05-18T02:16:21.797418+00:00","updated_at":"2026-05-18T02:16:21.797418+00:00"}