{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ON6ZCMCL4WLHITP4NKRLCYAC4S","short_pith_number":"pith:ON6ZCMCL","schema_version":"1.0","canonical_sha256":"737d91304be596744dfc6aa2b16002e4b9526bb852e740c7ad168df057c32005","source":{"kind":"arxiv","id":"1307.6657","version":1},"attestation_state":"computed","paper":{"title":"A Note on Resistance of NPT to Mixture of Separable States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Bobo Hua, Ming-Jing Zhao, Shao-Ming Fei, Xiu-Hong Gao","submitted_at":"2013-07-25T08:16:10Z","abstract_excerpt":"We study the stability of NPT property of an arbitrary pure entangled state under the mixture of arbitrary pure separable states. For bipartite pure states with Schmidt number $n$ $(n>1)$ which is NPT, we show that this state is still NPT when it is mixed with no more than $\\frac{n(n-1)}{2}-1$ arbitrary pure separable states. This result is generalized to multipartite case."},"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":"1307.6657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-07-25T08:16:10Z","cross_cats_sorted":[],"title_canon_sha256":"26b4b11513aa611a74f07c59ee985eae099b66cd48c914000b6ef15f1cf65f8b","abstract_canon_sha256":"c4b00269b68fecc8c75732595f3897398b943d8c86766eccba2e675d4dcd25ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:05.771492Z","signature_b64":"d3+bSd95f+JwG1qFWDNeXZLNcv8f3Ua1OtJ8ZBB984nnEdIeVTGJysv9faACzQln75DLt+xT2OTFBmbnoU8JBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"737d91304be596744dfc6aa2b16002e4b9526bb852e740c7ad168df057c32005","last_reissued_at":"2026-05-18T01:34:05.770985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:05.770985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Resistance of NPT to Mixture of Separable States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Bobo Hua, Ming-Jing Zhao, Shao-Ming Fei, Xiu-Hong Gao","submitted_at":"2013-07-25T08:16:10Z","abstract_excerpt":"We study the stability of NPT property of an arbitrary pure entangled state under the mixture of arbitrary pure separable states. For bipartite pure states with Schmidt number $n$ $(n>1)$ which is NPT, we show that this state is still NPT when it is mixed with no more than $\\frac{n(n-1)}{2}-1$ arbitrary pure separable states. This result is generalized to multipartite case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6657","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":"1307.6657","created_at":"2026-05-18T01:34:05.771065+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.6657v1","created_at":"2026-05-18T01:34:05.771065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6657","created_at":"2026-05-18T01:34:05.771065+00:00"},{"alias_kind":"pith_short_12","alias_value":"ON6ZCMCL4WLH","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"ON6ZCMCL4WLHITP4","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"ON6ZCMCL","created_at":"2026-05-18T12:27:54.935989+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/ON6ZCMCL4WLHITP4NKRLCYAC4S","json":"https://pith.science/pith/ON6ZCMCL4WLHITP4NKRLCYAC4S.json","graph_json":"https://pith.science/api/pith-number/ON6ZCMCL4WLHITP4NKRLCYAC4S/graph.json","events_json":"https://pith.science/api/pith-number/ON6ZCMCL4WLHITP4NKRLCYAC4S/events.json","paper":"https://pith.science/paper/ON6ZCMCL"},"agent_actions":{"view_html":"https://pith.science/pith/ON6ZCMCL4WLHITP4NKRLCYAC4S","download_json":"https://pith.science/pith/ON6ZCMCL4WLHITP4NKRLCYAC4S.json","view_paper":"https://pith.science/paper/ON6ZCMCL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.6657&json=true","fetch_graph":"https://pith.science/api/pith-number/ON6ZCMCL4WLHITP4NKRLCYAC4S/graph.json","fetch_events":"https://pith.science/api/pith-number/ON6ZCMCL4WLHITP4NKRLCYAC4S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ON6ZCMCL4WLHITP4NKRLCYAC4S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ON6ZCMCL4WLHITP4NKRLCYAC4S/action/storage_attestation","attest_author":"https://pith.science/pith/ON6ZCMCL4WLHITP4NKRLCYAC4S/action/author_attestation","sign_citation":"https://pith.science/pith/ON6ZCMCL4WLHITP4NKRLCYAC4S/action/citation_signature","submit_replication":"https://pith.science/pith/ON6ZCMCL4WLHITP4NKRLCYAC4S/action/replication_record"}},"created_at":"2026-05-18T01:34:05.771065+00:00","updated_at":"2026-05-18T01:34:05.771065+00:00"}