{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:RP57TNJJOACQGOP6YOWAZV27UB","short_pith_number":"pith:RP57TNJJ","schema_version":"1.0","canonical_sha256":"8bfbf9b52970050339fec3ac0cd75fa0415e7eccba447de5023924529b905c0f","source":{"kind":"arxiv","id":"1901.02312","version":1},"attestation_state":"computed","paper":{"title":"A hierarchy of entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger diagonal states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Li-zhen Jiang, Xiao-Yu Chen","submitted_at":"2019-01-08T14:01:56Z","abstract_excerpt":"With a two step optimization method of entanglement witness, we analytically propose a set of necessary and sufficient entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger (GHZ) diagonal states. The criterion set contains four criteria. Two of them are linear with density matrix elements. The other two criteria are nonlinear with density matrix elements. The criterion set has a nest structure. A proper subset of the criteria is necessary and sufficient for the entanglement of a proper subset of the states. We illustrate the nest structure of criterion set with the general"},"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":"1901.02312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-01-08T14:01:56Z","cross_cats_sorted":[],"title_canon_sha256":"2f762f962d2efc91a4dd6acaaa0ae73ec310e056e29dfe550ebf836d0a1820cf","abstract_canon_sha256":"490aa938d957b520833486e583e495a5270709d9fff68ac0be2294837d8212c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:43.602754Z","signature_b64":"qPOGl+e2WA6cQMSqoKwmuwh1nGANSK/8e0Dlmdg3gEPO7vL52tSC+2y6sYPIJmmjMQPwsKvSnFc7GIMDhOraCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bfbf9b52970050339fec3ac0cd75fa0415e7eccba447de5023924529b905c0f","last_reissued_at":"2026-05-17T23:56:43.602329Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:43.602329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A hierarchy of entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger diagonal states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Li-zhen Jiang, Xiao-Yu Chen","submitted_at":"2019-01-08T14:01:56Z","abstract_excerpt":"With a two step optimization method of entanglement witness, we analytically propose a set of necessary and sufficient entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger (GHZ) diagonal states. The criterion set contains four criteria. Two of them are linear with density matrix elements. The other two criteria are nonlinear with density matrix elements. The criterion set has a nest structure. A proper subset of the criteria is necessary and sufficient for the entanglement of a proper subset of the states. We illustrate the nest structure of criterion set with the general"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02312","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":"1901.02312","created_at":"2026-05-17T23:56:43.602392+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.02312v1","created_at":"2026-05-17T23:56:43.602392+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02312","created_at":"2026-05-17T23:56:43.602392+00:00"},{"alias_kind":"pith_short_12","alias_value":"RP57TNJJOACQ","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"RP57TNJJOACQGOP6","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"RP57TNJJ","created_at":"2026-05-18T12:33:27.125529+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/RP57TNJJOACQGOP6YOWAZV27UB","json":"https://pith.science/pith/RP57TNJJOACQGOP6YOWAZV27UB.json","graph_json":"https://pith.science/api/pith-number/RP57TNJJOACQGOP6YOWAZV27UB/graph.json","events_json":"https://pith.science/api/pith-number/RP57TNJJOACQGOP6YOWAZV27UB/events.json","paper":"https://pith.science/paper/RP57TNJJ"},"agent_actions":{"view_html":"https://pith.science/pith/RP57TNJJOACQGOP6YOWAZV27UB","download_json":"https://pith.science/pith/RP57TNJJOACQGOP6YOWAZV27UB.json","view_paper":"https://pith.science/paper/RP57TNJJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.02312&json=true","fetch_graph":"https://pith.science/api/pith-number/RP57TNJJOACQGOP6YOWAZV27UB/graph.json","fetch_events":"https://pith.science/api/pith-number/RP57TNJJOACQGOP6YOWAZV27UB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RP57TNJJOACQGOP6YOWAZV27UB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RP57TNJJOACQGOP6YOWAZV27UB/action/storage_attestation","attest_author":"https://pith.science/pith/RP57TNJJOACQGOP6YOWAZV27UB/action/author_attestation","sign_citation":"https://pith.science/pith/RP57TNJJOACQGOP6YOWAZV27UB/action/citation_signature","submit_replication":"https://pith.science/pith/RP57TNJJOACQGOP6YOWAZV27UB/action/replication_record"}},"created_at":"2026-05-17T23:56:43.602392+00:00","updated_at":"2026-05-17T23:56:43.602392+00:00"}