{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:THNKSUDIUABHCSZ4NUCXQYXSKJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5e57b94cbbe9bb39d4dfd8fadbe9e2e9b57964f2c18d9be7aa2fa3a4131dd151","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2015-01-26T14:04:09Z","title_canon_sha256":"0b403db3cdf2fe6f34517032338d9052c984e6f1210c9b5fe01bc41439317f85"},"schema_version":"1.0","source":{"id":"1501.06400","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06400","created_at":"2026-05-18T01:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06400v2","created_at":"2026-05-18T01:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06400","created_at":"2026-05-18T01:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"THNKSUDIUABH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"THNKSUDIUABHCSZ4","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"THNKSUDI","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:2ac9b9b1e6477fc751aaec553196a45f6fac31f1de254cddb4f810793688934e","target":"graph","created_at":"2026-05-18T01:59:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"An entangled basis with fixed Schmidt number $k$ (EBk) is a set of orthonormal basis states with the same Schmidt number $k$ in a product Hilbert space $\\mathbb{C}^d\\otimes\\mathbb{C}^{d'}$. It is a generalization of both the product basis and the maximally entangled basis. We show here that, for any $k\\leq\\min\\{d,d'\\}$, EBk exists in $\\mathbb{C}^d\\otimes\\mathbb{C}^{d'}$ for any $d$ and $d'$. Consequently, general methods of constructing SEBk (EBk with the same Schmidt coefficients) and EBk (but not SEBk) are proposed. Moreover, we extend the concept of EBk to multipartite case and find out tha","authors_text":"Shengjun Wu, Shuanping Du, Xiulan Li, Yu Guo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2015-01-26T14:04:09Z","title":"Entangled bases with fixed Schmidt number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06400","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b8b98b3badb2e7887bafe42c87e62ac41eea755b48a3412315dc7ad30739914d","target":"record","created_at":"2026-05-18T01:59:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5e57b94cbbe9bb39d4dfd8fadbe9e2e9b57964f2c18d9be7aa2fa3a4131dd151","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2015-01-26T14:04:09Z","title_canon_sha256":"0b403db3cdf2fe6f34517032338d9052c984e6f1210c9b5fe01bc41439317f85"},"schema_version":"1.0","source":{"id":"1501.06400","kind":"arxiv","version":2}},"canonical_sha256":"99daa95068a002714b3c6d057862f2525b46e0827a0405c35c22d45ed7da89f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99daa95068a002714b3c6d057862f2525b46e0827a0405c35c22d45ed7da89f5","first_computed_at":"2026-05-18T01:59:57.822381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:57.822381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3svduBHj5UN1mvysGPR77x3M9cCT7CTbB6APqs5K4mjFsJpCbWbaDZbf4tPSbROPWOXAg6W9oB7hMM5lyH51DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:57.822846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06400","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8b98b3badb2e7887bafe42c87e62ac41eea755b48a3412315dc7ad30739914d","sha256:2ac9b9b1e6477fc751aaec553196a45f6fac31f1de254cddb4f810793688934e"],"state_sha256":"2287c2786395d791dcf992230eaa387895f84b0b107498dafdf12fcaa787b229"}