{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YHZ33ADXHVNFGCDSUS6ILCPTD5","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":"b3d8a20aeb0265955b1f52265924dd7b471ab77a5c203b66b3777d489a3c03d2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-02T11:57:02Z","title_canon_sha256":"b87f0c20c40d63db9e7d856f2ccb61ecc60a467e8e1aaa99ae1bf9be7dde00e4"},"schema_version":"1.0","source":{"id":"1112.0437","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0437","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0437v2","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0437","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"YHZ33ADXHVNF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YHZ33ADXHVNFGCDS","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YHZ33ADX","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:0a4986ef7b95486f7a1a4e39c7f4cca35191260bafe85b0fad1b26141c3e8e08","target":"graph","created_at":"2026-05-18T03:59:02Z","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":"Majorana representation of quantum states by a constellation of n 'stars' (points on the sphere) can be used to describe any pure state of a simple system of dimension n+1 or a permutation symmetric pure state of a composite system consisting of n qubits. We analyze the variance of the distribution of the stars, which can serve as a measure of the degree of non-coherence for simple systems, or an entanglement measure for composed systems. Dynamics of the Majorana points induced by a unitary dynamics of the pure state is investigated.","authors_text":"Karol \\.Zyczkowski, Marek Ku\\'s, Wojciech Ganczarek","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-02T11:57:02Z","title":"Barycentric measure of quantum entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0437","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:f07317808c5b4a3979c0fc8334dba3a67c76e5692dc49a018acdb39dbb5955eb","target":"record","created_at":"2026-05-18T03:59:02Z","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":"b3d8a20aeb0265955b1f52265924dd7b471ab77a5c203b66b3777d489a3c03d2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-02T11:57:02Z","title_canon_sha256":"b87f0c20c40d63db9e7d856f2ccb61ecc60a467e8e1aaa99ae1bf9be7dde00e4"},"schema_version":"1.0","source":{"id":"1112.0437","kind":"arxiv","version":2}},"canonical_sha256":"c1f3bd80773d5a530872a4bc8589f31f4caf569dba6925ad1183f797bb1b42f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1f3bd80773d5a530872a4bc8589f31f4caf569dba6925ad1183f797bb1b42f9","first_computed_at":"2026-05-18T03:59:02.937454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:02.937454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jxYOvpaAVZMqqwUKYEDFr3prwxwDNmYVxLT16PyBzOLB6Mm+pmglD2lKQcI0MHFFgbhuQHReb0rkIra4wrgfBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:02.938144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0437","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f07317808c5b4a3979c0fc8334dba3a67c76e5692dc49a018acdb39dbb5955eb","sha256:0a4986ef7b95486f7a1a4e39c7f4cca35191260bafe85b0fad1b26141c3e8e08"],"state_sha256":"27a92f6f9821f7a2f0fa8b29c361d4741280b345369ddc33e4c926756841b9cc"}