{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2K6OHXLLLEXVCIBJV5FUIHT3JL","short_pith_number":"pith:2K6OHXLL","schema_version":"1.0","canonical_sha256":"d2bce3dd6b592f512029af4b441e7b4adbfb5ebdd1eb3d87a599d8be42676bc0","source":{"kind":"arxiv","id":"1606.06184","version":2},"attestation_state":"computed","paper":{"title":"Geometric approach to entanglement quantification with polynomial measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Bartosz Regula, Gerardo Adesso","submitted_at":"2016-06-20T15:52:19Z","abstract_excerpt":"We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides novel insight into the properties of entanglement and allows us to relate different polynomial measures to each other, simplifying their quantification. In particular, unveiling and exploiting the geometric structure of the concurrence for two qubits, we show that the convex roof of any polynomial measure of entanglement can be quantified exactly for all rank-2 states of an arbitrary number of"},"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":"1606.06184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-20T15:52:19Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1c306ec402641ed0de3e2bc727096631d30d95d261fa2d9cb0be7084ceec001a","abstract_canon_sha256":"69a161e6dd58df3bc10fb02783758afd59cabec9cebd55fc1e041f60e3cc7348"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:23.687018Z","signature_b64":"Jb35fA/SXWkW8bv+we7G8u2VKN7WTK+N7sNdpRa8It1pwQEwwnSw8ukF5UxmMVlHpcvGF+ZtpsvMHs5ViRWwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2bce3dd6b592f512029af4b441e7b4adbfb5ebdd1eb3d87a599d8be42676bc0","last_reissued_at":"2026-05-18T01:08:23.686364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:23.686364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric approach to entanglement quantification with polynomial measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Bartosz Regula, Gerardo Adesso","submitted_at":"2016-06-20T15:52:19Z","abstract_excerpt":"We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides novel insight into the properties of entanglement and allows us to relate different polynomial measures to each other, simplifying their quantification. In particular, unveiling and exploiting the geometric structure of the concurrence for two qubits, we show that the convex roof of any polynomial measure of entanglement can be quantified exactly for all rank-2 states of an arbitrary number of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06184","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":"1606.06184","created_at":"2026-05-18T01:08:23.686467+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.06184v2","created_at":"2026-05-18T01:08:23.686467+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06184","created_at":"2026-05-18T01:08:23.686467+00:00"},{"alias_kind":"pith_short_12","alias_value":"2K6OHXLLLEXV","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"2K6OHXLLLEXVCIBJ","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"2K6OHXLL","created_at":"2026-05-18T12:29:55.572404+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/2K6OHXLLLEXVCIBJV5FUIHT3JL","json":"https://pith.science/pith/2K6OHXLLLEXVCIBJV5FUIHT3JL.json","graph_json":"https://pith.science/api/pith-number/2K6OHXLLLEXVCIBJV5FUIHT3JL/graph.json","events_json":"https://pith.science/api/pith-number/2K6OHXLLLEXVCIBJV5FUIHT3JL/events.json","paper":"https://pith.science/paper/2K6OHXLL"},"agent_actions":{"view_html":"https://pith.science/pith/2K6OHXLLLEXVCIBJV5FUIHT3JL","download_json":"https://pith.science/pith/2K6OHXLLLEXVCIBJV5FUIHT3JL.json","view_paper":"https://pith.science/paper/2K6OHXLL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.06184&json=true","fetch_graph":"https://pith.science/api/pith-number/2K6OHXLLLEXVCIBJV5FUIHT3JL/graph.json","fetch_events":"https://pith.science/api/pith-number/2K6OHXLLLEXVCIBJV5FUIHT3JL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2K6OHXLLLEXVCIBJV5FUIHT3JL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2K6OHXLLLEXVCIBJV5FUIHT3JL/action/storage_attestation","attest_author":"https://pith.science/pith/2K6OHXLLLEXVCIBJV5FUIHT3JL/action/author_attestation","sign_citation":"https://pith.science/pith/2K6OHXLLLEXVCIBJV5FUIHT3JL/action/citation_signature","submit_replication":"https://pith.science/pith/2K6OHXLLLEXVCIBJV5FUIHT3JL/action/replication_record"}},"created_at":"2026-05-18T01:08:23.686467+00:00","updated_at":"2026-05-18T01:08:23.686467+00:00"}