{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:HC5XLGHEEGUSFHVES3FNJRKOJ5","short_pith_number":"pith:HC5XLGHE","schema_version":"1.0","canonical_sha256":"38bb7598e421a9229ea496cad4c54e4f65a78f142c59b573d3e6fdd55665f355","source":{"kind":"arxiv","id":"0906.2731","version":1},"attestation_state":"computed","paper":{"title":"The power of symmetric extensions for entanglement detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Martin B. Plenio, Masaki Owari, Miguel Navascues","submitted_at":"2009-06-15T15:56:14Z","abstract_excerpt":"In this paper, we present new progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state admitting an N Bose symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from N Bose symmetric extensions with Positive Partial Transpose (PPT) decreases at least as fast as O(1/N^2). From these results, we derive upper bounds on the time and space complexity of the weak membership probl"},"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":"0906.2731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-06-15T15:56:14Z","cross_cats_sorted":[],"title_canon_sha256":"ef08d197239fb8505e5de98538b495b099c409f4af2a5530c0af556f30fe4c36","abstract_canon_sha256":"958f9990e052b5fc2a2cb4df93b628c05c0a49b3ecdf69b750ee52b82b44a6a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:59.429472Z","signature_b64":"i3ZH9HtdvWYlZoojRttdC6y3oozDWuZ+cKnO85D+bGLDwm0DnrlWKZnFnrpGdyKpi8NtPSLxM9DH/zsI2GO/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38bb7598e421a9229ea496cad4c54e4f65a78f142c59b573d3e6fdd55665f355","last_reissued_at":"2026-05-18T03:23:59.428719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:59.428719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The power of symmetric extensions for entanglement detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Martin B. Plenio, Masaki Owari, Miguel Navascues","submitted_at":"2009-06-15T15:56:14Z","abstract_excerpt":"In this paper, we present new progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state admitting an N Bose symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from N Bose symmetric extensions with Positive Partial Transpose (PPT) decreases at least as fast as O(1/N^2). From these results, we derive upper bounds on the time and space complexity of the weak membership probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2731","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0906.2731","created_at":"2026-05-18T03:23:59.428866+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.2731v1","created_at":"2026-05-18T03:23:59.428866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2731","created_at":"2026-05-18T03:23:59.428866+00:00"},{"alias_kind":"pith_short_12","alias_value":"HC5XLGHEEGUS","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"HC5XLGHEEGUSFHVE","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"HC5XLGHE","created_at":"2026-05-18T12:25:59.703012+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.16249","citing_title":"The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems","ref_index":27,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HC5XLGHEEGUSFHVES3FNJRKOJ5","json":"https://pith.science/pith/HC5XLGHEEGUSFHVES3FNJRKOJ5.json","graph_json":"https://pith.science/api/pith-number/HC5XLGHEEGUSFHVES3FNJRKOJ5/graph.json","events_json":"https://pith.science/api/pith-number/HC5XLGHEEGUSFHVES3FNJRKOJ5/events.json","paper":"https://pith.science/paper/HC5XLGHE"},"agent_actions":{"view_html":"https://pith.science/pith/HC5XLGHEEGUSFHVES3FNJRKOJ5","download_json":"https://pith.science/pith/HC5XLGHEEGUSFHVES3FNJRKOJ5.json","view_paper":"https://pith.science/paper/HC5XLGHE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.2731&json=true","fetch_graph":"https://pith.science/api/pith-number/HC5XLGHEEGUSFHVES3FNJRKOJ5/graph.json","fetch_events":"https://pith.science/api/pith-number/HC5XLGHEEGUSFHVES3FNJRKOJ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HC5XLGHEEGUSFHVES3FNJRKOJ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HC5XLGHEEGUSFHVES3FNJRKOJ5/action/storage_attestation","attest_author":"https://pith.science/pith/HC5XLGHEEGUSFHVES3FNJRKOJ5/action/author_attestation","sign_citation":"https://pith.science/pith/HC5XLGHEEGUSFHVES3FNJRKOJ5/action/citation_signature","submit_replication":"https://pith.science/pith/HC5XLGHEEGUSFHVES3FNJRKOJ5/action/replication_record"}},"created_at":"2026-05-18T03:23:59.428866+00:00","updated_at":"2026-05-18T03:23:59.428866+00:00"}