{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IMGI77YWOHDFERMXAZMLIWUU6R","short_pith_number":"pith:IMGI77YW","schema_version":"1.0","canonical_sha256":"430c8fff1671c65245970658b45a94f455402b907c2a6a2c0941c64e18d329b7","source":{"kind":"arxiv","id":"1505.06261","version":1},"attestation_state":"computed","paper":{"title":"Entanglement of Four-Qubit Rank-$2$ Mixed States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"DaeKil Park, Eylee Jung","submitted_at":"2015-05-23T01:57:07Z","abstract_excerpt":"It is known that there are three maximally entangled states $\\ket{\\Phi_1} = (\\ket{0000} + \\ket{1111}) / \\sqrt{2}$, $\\ket{\\Phi_2} = (\\sqrt{2} \\ket{1111} + \\ket{1000} + \\ket{0100} + \\ket{0010} + \\ket{0001}) / \\sqrt{6}$, and $\\ket{\\Phi_3} = (\\ket{1111} + \\ket{1100} + \\ket{0010} + \\ket{0001}) / 2$ in four-qubit system. It is also known that there are three independent measures ${\\cal F}^{(4)}_j \\hspace{.2cm} (j=1,2,3)$ for true four-way quantum entanglement in the same system. In this paper we compute ${\\cal F}^{(4)}_j$ and their corresponding linear monotones ${\\cal G}^{(4)}_j$ for three rank-two"},"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":"1505.06261","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-23T01:57:07Z","cross_cats_sorted":[],"title_canon_sha256":"84b8360d735997cc0a767e17f1b798a6fc6fe7e857e556cb9f11bb6721b29ab3","abstract_canon_sha256":"4d6158dc128d3bcd13a36578205bae3220d83fc2f90b715a9d1a8bd3af7367a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:47.753770Z","signature_b64":"kS9P4ZThCZhHPPG0VJoNVN30MS7UOS3ygK85SINDYT6GmjPNJqmNJgNUYcBUjVqRRyUjr+xqPtBOLVd+1ditDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"430c8fff1671c65245970658b45a94f455402b907c2a6a2c0941c64e18d329b7","last_reissued_at":"2026-05-18T02:03:47.752962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:47.752962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entanglement of Four-Qubit Rank-$2$ Mixed States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"DaeKil Park, Eylee Jung","submitted_at":"2015-05-23T01:57:07Z","abstract_excerpt":"It is known that there are three maximally entangled states $\\ket{\\Phi_1} = (\\ket{0000} + \\ket{1111}) / \\sqrt{2}$, $\\ket{\\Phi_2} = (\\sqrt{2} \\ket{1111} + \\ket{1000} + \\ket{0100} + \\ket{0010} + \\ket{0001}) / \\sqrt{6}$, and $\\ket{\\Phi_3} = (\\ket{1111} + \\ket{1100} + \\ket{0010} + \\ket{0001}) / 2$ in four-qubit system. It is also known that there are three independent measures ${\\cal F}^{(4)}_j \\hspace{.2cm} (j=1,2,3)$ for true four-way quantum entanglement in the same system. In this paper we compute ${\\cal F}^{(4)}_j$ and their corresponding linear monotones ${\\cal G}^{(4)}_j$ for three rank-two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06261","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":"1505.06261","created_at":"2026-05-18T02:03:47.753094+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06261v1","created_at":"2026-05-18T02:03:47.753094+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06261","created_at":"2026-05-18T02:03:47.753094+00:00"},{"alias_kind":"pith_short_12","alias_value":"IMGI77YWOHDF","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"IMGI77YWOHDFERMX","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"IMGI77YW","created_at":"2026-05-18T12:29:25.134429+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/IMGI77YWOHDFERMXAZMLIWUU6R","json":"https://pith.science/pith/IMGI77YWOHDFERMXAZMLIWUU6R.json","graph_json":"https://pith.science/api/pith-number/IMGI77YWOHDFERMXAZMLIWUU6R/graph.json","events_json":"https://pith.science/api/pith-number/IMGI77YWOHDFERMXAZMLIWUU6R/events.json","paper":"https://pith.science/paper/IMGI77YW"},"agent_actions":{"view_html":"https://pith.science/pith/IMGI77YWOHDFERMXAZMLIWUU6R","download_json":"https://pith.science/pith/IMGI77YWOHDFERMXAZMLIWUU6R.json","view_paper":"https://pith.science/paper/IMGI77YW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06261&json=true","fetch_graph":"https://pith.science/api/pith-number/IMGI77YWOHDFERMXAZMLIWUU6R/graph.json","fetch_events":"https://pith.science/api/pith-number/IMGI77YWOHDFERMXAZMLIWUU6R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IMGI77YWOHDFERMXAZMLIWUU6R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IMGI77YWOHDFERMXAZMLIWUU6R/action/storage_attestation","attest_author":"https://pith.science/pith/IMGI77YWOHDFERMXAZMLIWUU6R/action/author_attestation","sign_citation":"https://pith.science/pith/IMGI77YWOHDFERMXAZMLIWUU6R/action/citation_signature","submit_replication":"https://pith.science/pith/IMGI77YWOHDFERMXAZMLIWUU6R/action/replication_record"}},"created_at":"2026-05-18T02:03:47.753094+00:00","updated_at":"2026-05-18T02:03:47.753094+00:00"}