{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IERTOEQA75EH65MRITK6YDPTT2","short_pith_number":"pith:IERTOEQA","schema_version":"1.0","canonical_sha256":"4123371200ff487f759144d5ec0df39e9e696e763ac22b2321b1aceee6bf261f","source":{"kind":"arxiv","id":"1611.09586","version":2},"attestation_state":"computed","paper":{"title":"Volume of the set of locally diagonalizable bipartite states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Lin Zhang, Seunghun Hong","submitted_at":"2016-11-29T12:18:08Z","abstract_excerpt":"The purpose of this article is to investigate the geometry of the set of locally diagonalizable bipartite quantum states. We have the following new results: the Hilbert-Schmidt volume of all locally diagonalizable states, and a necessary and sufficient condition for local diagonalizability in the qubit-qubit case. Besides, we partition the set of all locally diagonalizable states as local unitary orbits (or coadjoint orbits) of diagonal forms. It is well-known that the Riemannian volume of a coadjoint orbit for a regular point in a specified Weyl chamber can be calculated by Harish-Chandra's v"},"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":"1611.09586","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-11-29T12:18:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"eadf742e3f3df9bcdad51d7868eaae3e236a8345aa1b386df2fa2bccf0e77af8","abstract_canon_sha256":"b9dc3fcc218332c0d606c272e40057570148e728c6d0c838dc1650dee28beb98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:55.737579Z","signature_b64":"Jy9l0L79Gvz2JVgeyK70QEEmAPU/Wa3QyZwKWKGwWIcfvtpMA7zs/MbgyU+skGYFHudnUUQFUZ06I2wSHCNCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4123371200ff487f759144d5ec0df39e9e696e763ac22b2321b1aceee6bf261f","last_reissued_at":"2026-05-18T00:07:55.736910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:55.736910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Volume of the set of locally diagonalizable bipartite states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Lin Zhang, Seunghun Hong","submitted_at":"2016-11-29T12:18:08Z","abstract_excerpt":"The purpose of this article is to investigate the geometry of the set of locally diagonalizable bipartite quantum states. We have the following new results: the Hilbert-Schmidt volume of all locally diagonalizable states, and a necessary and sufficient condition for local diagonalizability in the qubit-qubit case. Besides, we partition the set of all locally diagonalizable states as local unitary orbits (or coadjoint orbits) of diagonal forms. It is well-known that the Riemannian volume of a coadjoint orbit for a regular point in a specified Weyl chamber can be calculated by Harish-Chandra's v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09586","kind":"arxiv","version":2},"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":"1611.09586","created_at":"2026-05-18T00:07:55.737013+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.09586v2","created_at":"2026-05-18T00:07:55.737013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09586","created_at":"2026-05-18T00:07:55.737013+00:00"},{"alias_kind":"pith_short_12","alias_value":"IERTOEQA75EH","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IERTOEQA75EH65MR","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IERTOEQA","created_at":"2026-05-18T12:30:22.444734+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/IERTOEQA75EH65MRITK6YDPTT2","json":"https://pith.science/pith/IERTOEQA75EH65MRITK6YDPTT2.json","graph_json":"https://pith.science/api/pith-number/IERTOEQA75EH65MRITK6YDPTT2/graph.json","events_json":"https://pith.science/api/pith-number/IERTOEQA75EH65MRITK6YDPTT2/events.json","paper":"https://pith.science/paper/IERTOEQA"},"agent_actions":{"view_html":"https://pith.science/pith/IERTOEQA75EH65MRITK6YDPTT2","download_json":"https://pith.science/pith/IERTOEQA75EH65MRITK6YDPTT2.json","view_paper":"https://pith.science/paper/IERTOEQA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.09586&json=true","fetch_graph":"https://pith.science/api/pith-number/IERTOEQA75EH65MRITK6YDPTT2/graph.json","fetch_events":"https://pith.science/api/pith-number/IERTOEQA75EH65MRITK6YDPTT2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IERTOEQA75EH65MRITK6YDPTT2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IERTOEQA75EH65MRITK6YDPTT2/action/storage_attestation","attest_author":"https://pith.science/pith/IERTOEQA75EH65MRITK6YDPTT2/action/author_attestation","sign_citation":"https://pith.science/pith/IERTOEQA75EH65MRITK6YDPTT2/action/citation_signature","submit_replication":"https://pith.science/pith/IERTOEQA75EH65MRITK6YDPTT2/action/replication_record"}},"created_at":"2026-05-18T00:07:55.737013+00:00","updated_at":"2026-05-18T00:07:55.737013+00:00"}