{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ECI5ORYTI53SK7Z4F2JHRTFVOA","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":"d2367ac7983518e01891a951ce607d1dedf627a2072f18a2975836f772a17787","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-01-18T00:02:33Z","title_canon_sha256":"e63ae8a4cdac86bf7400c2a2f1eb882e289004cb87365b331d7053321ae45dfe"},"schema_version":"1.0","source":{"id":"1401.4495","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4495","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4495v3","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4495","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"ECI5ORYTI53S","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"ECI5ORYTI53SK7Z4","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"ECI5ORYT","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:a6e4c92c596e9e83e556698b9a2faa03aecce3d3608ba8ec39f267954437a890","target":"graph","created_at":"2026-05-18T02:51:41Z","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":"We consider the concept of \"the permutationally invariant (PI) part of a density matrix,\" which has proven very useful for both efficient quantum state estimation and entanglement characterization of $N$-qubit systems. We show here that the concept is, in fact, basis-dependent, but that this basis dependence makes it an even more powerful concept than has been appreciated so far. By considering the PI part $\\rho^{{\\rm PI}}$ of a general (mixed) $N$-qubit state $\\rho$, we obtain: (i) strong bounds on quantitative nonseparability measures, (ii) a whole hierarchy of multi-partite separability cri","authors_text":"Fengli Yan, S.J. van Enk, Ting Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-01-18T00:02:33Z","title":"On the permutationally invariant part of a density matrix and nonseparability of N-qubit states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4495","kind":"arxiv","version":3},"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:c7ac53cc0ba0fd0f3f05f7604d93c73c42d170d9c3d419dd881137c74c769fe3","target":"record","created_at":"2026-05-18T02:51:41Z","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":"d2367ac7983518e01891a951ce607d1dedf627a2072f18a2975836f772a17787","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-01-18T00:02:33Z","title_canon_sha256":"e63ae8a4cdac86bf7400c2a2f1eb882e289004cb87365b331d7053321ae45dfe"},"schema_version":"1.0","source":{"id":"1401.4495","kind":"arxiv","version":3}},"canonical_sha256":"2091d747134777257f3c2e9278ccb5701b0d998d049adc666c062c0a9a383aea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2091d747134777257f3c2e9278ccb5701b0d998d049adc666c062c0a9a383aea","first_computed_at":"2026-05-18T02:51:41.694627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:41.694627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6q5wmlH4k43sEKNREozRsPLyflD3McwxTiytCgo2qh++Nz0KDytxnC5cFP0Zu+mZP/nvBHYeplP16Mb4Ho5+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:41.695199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4495","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7ac53cc0ba0fd0f3f05f7604d93c73c42d170d9c3d419dd881137c74c769fe3","sha256:a6e4c92c596e9e83e556698b9a2faa03aecce3d3608ba8ec39f267954437a890"],"state_sha256":"b9b12bf114587066838662829190a8885ca3a716441f5c0c7fef29438fb7cf7f"}