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An operational method to construct UMEBs containing $d(d^{\\prime}-1)$ maximally entangled vectors is established, and two UMEBs in \\(\\mathbb {C}^{5}\\otimes \\mathbb {C}^{6}\\) and \\(\\mathbb {C}^{5}\\otimes \\mathbb {C}^{12}\\) are given as examples. Furthermore, a systematic way of constructing UMEBs containing $d(d^{\\prime}-r)$ maximally entangled vectors in \\(\\mathbb {C}^{d}\\otimes \\mathbb {C}^{d^{\\prime}}\\) is presented for $r=1,2,\\cdots, d-1$. Correspondingly, two UMEBs in \\("},"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":"1802.07594","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-02-21T14:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"178e1b0b96540728d504670e4b5d6f79c18b50b73645ab73af1824f55883f659","abstract_canon_sha256":"b757d7298bfeb3f2665b76b3ec4d5480836aa5b87af0d00bd47a7a4bd053565d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:49.845331Z","signature_b64":"Tkxs6YMx2PozFBF11MhiyRqSpSd4fLGWHOHUwdUaMnu8mkB48V/xcwXj00cj/xPeGgxH3yWUl9+8FpodcQUADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b02a9f1902e77607cd0cd79cdb6337a420365328ad282742e0091ab8bfbc3a2","last_reissued_at":"2026-05-18T00:22:49.844927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:49.844927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructions of Unextendible Maximally Entangled Bases in \\(\\mathbb {C}^{d}\\otimes \\mathbb {C}^{d^{\\prime}}\\)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Gui-Jun Zhang, Shao-Ming Fei, Xin-Lei Yong, Yi-Fan Han, Yuan-hong Tao","submitted_at":"2018-02-21T14:51:32Z","abstract_excerpt":"We study unextendible maximally entangled bases (UMEBs) in \\(\\mathbb {C}^{d}\\otimes \\mathbb {C}^{d^{\\prime}}\\) ($d<d'$). An operational method to construct UMEBs containing $d(d^{\\prime}-1)$ maximally entangled vectors is established, and two UMEBs in \\(\\mathbb {C}^{5}\\otimes \\mathbb {C}^{6}\\) and \\(\\mathbb {C}^{5}\\otimes \\mathbb {C}^{12}\\) are given as examples. Furthermore, a systematic way of constructing UMEBs containing $d(d^{\\prime}-r)$ maximally entangled vectors in \\(\\mathbb {C}^{d}\\otimes \\mathbb {C}^{d^{\\prime}}\\) is presented for $r=1,2,\\cdots, d-1$. Correspondingly, two UMEBs in \\("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07594","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":"1802.07594","created_at":"2026-05-18T00:22:49.844982+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.07594v1","created_at":"2026-05-18T00:22:49.844982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07594","created_at":"2026-05-18T00:22:49.844982+00:00"},{"alias_kind":"pith_short_12","alias_value":"HMBKT4MQFZ3W","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HMBKT4MQFZ3WA7GQ","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HMBKT4MQ","created_at":"2026-05-18T12:32:28.185984+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/HMBKT4MQFZ3WA7GQZV443NRTPJ","json":"https://pith.science/pith/HMBKT4MQFZ3WA7GQZV443NRTPJ.json","graph_json":"https://pith.science/api/pith-number/HMBKT4MQFZ3WA7GQZV443NRTPJ/graph.json","events_json":"https://pith.science/api/pith-number/HMBKT4MQFZ3WA7GQZV443NRTPJ/events.json","paper":"https://pith.science/paper/HMBKT4MQ"},"agent_actions":{"view_html":"https://pith.science/pith/HMBKT4MQFZ3WA7GQZV443NRTPJ","download_json":"https://pith.science/pith/HMBKT4MQFZ3WA7GQZV443NRTPJ.json","view_paper":"https://pith.science/paper/HMBKT4MQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.07594&json=true","fetch_graph":"https://pith.science/api/pith-number/HMBKT4MQFZ3WA7GQZV443NRTPJ/graph.json","fetch_events":"https://pith.science/api/pith-number/HMBKT4MQFZ3WA7GQZV443NRTPJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HMBKT4MQFZ3WA7GQZV443NRTPJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HMBKT4MQFZ3WA7GQZV443NRTPJ/action/storage_attestation","attest_author":"https://pith.science/pith/HMBKT4MQFZ3WA7GQZV443NRTPJ/action/author_attestation","sign_citation":"https://pith.science/pith/HMBKT4MQFZ3WA7GQZV443NRTPJ/action/citation_signature","submit_replication":"https://pith.science/pith/HMBKT4MQFZ3WA7GQZV443NRTPJ/action/replication_record"}},"created_at":"2026-05-18T00:22:49.844982+00:00","updated_at":"2026-05-18T00:22:49.844982+00:00"}