{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4GZPNFS5VZ6HXSEEGFK27TO2BO","short_pith_number":"pith:4GZPNFS5","schema_version":"1.0","canonical_sha256":"e1b2f6965dae7c7bc8843155afcdda0b9463baf74faba5bb6123ee3a16d37df4","source":{"kind":"arxiv","id":"1810.08932","version":1},"attestation_state":"computed","paper":{"title":"Constructing $2\\times2\\times4$ and $4\\times4$ unextendible product bases and positive-partial-transpose entangled states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kai Wang, Lijun Zhao, Lin Chen, Yi Shen, Yize Sun","submitted_at":"2018-10-21T12:30:38Z","abstract_excerpt":"The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in $\\cH=\\bbC^2\\ox\\bbC^2\\ox\\bbC^4$, three UPBs of size $9$ in $\\cK=\\bbC^4\\ox\\bbC^4$, and no UPB of size $7$ in $\\cH$ and $\\cK$. Furthermore we construct a 4-qubit positive-partial-transpose (PPT) entangled state $\\r$ of rank seven, and show that it is also a PPT entangled state in $\\cH$ and $\\cK$, respectively. We analytically derive the geometric measure of entanglement of a spec"},"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":"1810.08932","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-21T12:30:38Z","cross_cats_sorted":[],"title_canon_sha256":"9d83dd2e6cc2298598164f0118d3a01ec2028c138bb5e1c5f0534f2a7f0f12fc","abstract_canon_sha256":"a2e48c67ca04ea11d8b83011dcbff71c62726e8e80156d6e334b10566108c4f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:41.419368Z","signature_b64":"csvP8T/Ghz/684cPpqqd3TRSCfYjc623ecQYzdA48dQcwCRX9lZdQEMEuqqv0iCF6SVO9PTnPY7I5aDcFgRbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1b2f6965dae7c7bc8843155afcdda0b9463baf74faba5bb6123ee3a16d37df4","last_reissued_at":"2026-05-18T00:02:41.418937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:41.418937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructing $2\\times2\\times4$ and $4\\times4$ unextendible product bases and positive-partial-transpose entangled states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kai Wang, Lijun Zhao, Lin Chen, Yi Shen, Yize Sun","submitted_at":"2018-10-21T12:30:38Z","abstract_excerpt":"The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in $\\cH=\\bbC^2\\ox\\bbC^2\\ox\\bbC^4$, three UPBs of size $9$ in $\\cK=\\bbC^4\\ox\\bbC^4$, and no UPB of size $7$ in $\\cH$ and $\\cK$. Furthermore we construct a 4-qubit positive-partial-transpose (PPT) entangled state $\\r$ of rank seven, and show that it is also a PPT entangled state in $\\cH$ and $\\cK$, respectively. We analytically derive the geometric measure of entanglement of a spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08932","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":"1810.08932","created_at":"2026-05-18T00:02:41.419001+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.08932v1","created_at":"2026-05-18T00:02:41.419001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08932","created_at":"2026-05-18T00:02:41.419001+00:00"},{"alias_kind":"pith_short_12","alias_value":"4GZPNFS5VZ6H","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4GZPNFS5VZ6HXSEE","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4GZPNFS5","created_at":"2026-05-18T12:32:05.422762+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/4GZPNFS5VZ6HXSEEGFK27TO2BO","json":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO.json","graph_json":"https://pith.science/api/pith-number/4GZPNFS5VZ6HXSEEGFK27TO2BO/graph.json","events_json":"https://pith.science/api/pith-number/4GZPNFS5VZ6HXSEEGFK27TO2BO/events.json","paper":"https://pith.science/paper/4GZPNFS5"},"agent_actions":{"view_html":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO","download_json":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO.json","view_paper":"https://pith.science/paper/4GZPNFS5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.08932&json=true","fetch_graph":"https://pith.science/api/pith-number/4GZPNFS5VZ6HXSEEGFK27TO2BO/graph.json","fetch_events":"https://pith.science/api/pith-number/4GZPNFS5VZ6HXSEEGFK27TO2BO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/action/storage_attestation","attest_author":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/action/author_attestation","sign_citation":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/action/citation_signature","submit_replication":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/action/replication_record"}},"created_at":"2026-05-18T00:02:41.419001+00:00","updated_at":"2026-05-18T00:02:41.419001+00:00"}