{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UO3HKQEOXQCEY2YPOSGJFSZYUZ","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":"f793fdc9bc128641ddeb4d64e96adbe025b5bbdb24404afc246755f3ecc57ae8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-06T06:15:33Z","title_canon_sha256":"95316e7dd7c24e3e23dbb15d555e7ccb7b4816ebe6ab0ee1e1035fb55c521176"},"schema_version":"1.0","source":{"id":"1603.01792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01792","created_at":"2026-05-18T01:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01792v1","created_at":"2026-05-18T01:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01792","created_at":"2026-05-18T01:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"UO3HKQEOXQCE","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UO3HKQEOXQCEY2YP","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UO3HKQEO","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:72732a02a0791dc4668a1428e3b1bdb252aa7b088c9c2c4da9e7da18092110ef","target":"graph","created_at":"2026-05-18T01:16:40Z","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":"The practically useful criteria of separable states $\\rho=\\sum_{k}w_{k}\\rho_{k}$ in $d=2\\times2$ are discussed. The equality $G({\\bf a},{\\bf b})= 4[\\langle \\psi|P({\\bf a})\\otimes P({\\bf b})|\\psi\\rangle-\\langle \\psi|P({\\bf a})\\otimes{\\bf 1}|\\psi\\rangle\\langle \\psi|{\\bf 1}\\otimes P({\\bf b})|\\psi\\rangle]=0$ for any two projection operators $P({\\bf a})$ and $P({\\bf b})$ provides a necessary and sufficient separability criterion in the case of a separable pure state $\\rho=|\\psi\\rangle\\langle\\psi|$. We propose the separability criteria of mixed states, which are given by ${\\rm Tr}\\rho\\{{\\bf a}\\cdot ","authors_text":"C.H. Oh, Kazuo Fujikawa, Koichiro Umetsu, Sixia Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-06T06:15:33Z","title":"Separability criteria with angular and Hilbert space averages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01792","kind":"arxiv","version":1},"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:b22f3796c559c2be7a623e034ee670af3ad9aa4c7e9bd6a56f4e04da11d783a8","target":"record","created_at":"2026-05-18T01:16:40Z","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":"f793fdc9bc128641ddeb4d64e96adbe025b5bbdb24404afc246755f3ecc57ae8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-06T06:15:33Z","title_canon_sha256":"95316e7dd7c24e3e23dbb15d555e7ccb7b4816ebe6ab0ee1e1035fb55c521176"},"schema_version":"1.0","source":{"id":"1603.01792","kind":"arxiv","version":1}},"canonical_sha256":"a3b675408ebc044c6b0f748c92cb38a67896121b6ebe98130298cd6d652786ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3b675408ebc044c6b0f748c92cb38a67896121b6ebe98130298cd6d652786ce","first_computed_at":"2026-05-18T01:16:40.031270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:40.031270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nF+Z96ILiXVqXZnuAGUooE60yRpsibDL16Hu699A7t8Y3819lWdsgUgL2pIrtkvyiEQ+Q9Vv2R+pRDwJYsjYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:40.031922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b22f3796c559c2be7a623e034ee670af3ad9aa4c7e9bd6a56f4e04da11d783a8","sha256:72732a02a0791dc4668a1428e3b1bdb252aa7b088c9c2c4da9e7da18092110ef"],"state_sha256":"ac11a59d3199e04185a6dfd90e7780708a5b7192efdb144b5b30499068ffa951"}