{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:NZUYEUE6KVQETCBUPS6GOICB5Y","short_pith_number":"pith:NZUYEUE6","canonical_record":{"source":{"id":"quant-ph/0007081","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2000-07-21T09:32:14Z","cross_cats_sorted":[],"title_canon_sha256":"73dc09ffa917b04213bfc6dfb922b7899296986b0a4dcae489e6ea5eb16c939a","abstract_canon_sha256":"0db62244ebac137bbb562a243fb0b7c5961652f3e4a114bb2b492b9648e71e18"},"schema_version":"1.0"},"canonical_sha256":"6e6982509e55604988347cbc672041ee21a555040fb5ba741a724c5bcc4d19b5","source":{"kind":"arxiv","id":"quant-ph/0007081","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0007081","created_at":"2026-05-18T01:05:06Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0007081v3","created_at":"2026-05-18T01:05:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0007081","created_at":"2026-05-18T01:05:06Z"},{"alias_kind":"pith_short_12","alias_value":"NZUYEUE6KVQE","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"NZUYEUE6KVQETCBU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"NZUYEUE6","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:NZUYEUE6KVQETCBUPS6GOICB5Y","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0007081","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2000-07-21T09:32:14Z","cross_cats_sorted":[],"title_canon_sha256":"73dc09ffa917b04213bfc6dfb922b7899296986b0a4dcae489e6ea5eb16c939a","abstract_canon_sha256":"0db62244ebac137bbb562a243fb0b7c5961652f3e4a114bb2b492b9648e71e18"},"schema_version":"1.0"},"canonical_sha256":"6e6982509e55604988347cbc672041ee21a555040fb5ba741a724c5bcc4d19b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:06.821770Z","signature_b64":"aC/OGusDUc9E9oy3LMFqGKZ7zr+0dUINCBEME3dQG544M35VmA2CB4hM6nIp7c6kE0qIxKQhnhckLy3OHi7GBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e6982509e55604988347cbc672041ee21a555040fb5ba741a724c5bcc4d19b5","last_reissued_at":"2026-05-18T01:05:06.821125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:06.821125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0007081","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4oEE8rUJyewEeoK+GdVcBBDOpaZR1ohWSnxERgZ+7MXPVwzyLVifLIVdaakVK8pxf23qw37Wkm/0UKoyMrgYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:27:23.577291Z"},"content_sha256":"cb85a0a9944cece58a0dba65bd7cb7e9698f152fd423c4a4f2d510d3b7138e92","schema_version":"1.0","event_id":"sha256:cb85a0a9944cece58a0dba65bd7cb7e9698f152fd423c4a4f2d510d3b7138e92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:NZUYEUE6KVQETCBUPS6GOICB5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"H.-J. Briegel, J. Eisert","submitted_at":"2000-07-21T09:32:14Z","abstract_excerpt":"We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on the full state space and is shown to be an entanglement monotone, that is, it cannot increase under local quantum operations with classical communication and under mixing. For a large class of mixed states this measure of entanglement can be calculated exactly, and it provides a detailed classification of mixed states."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0007081","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfUEfps9oa9bnhQGcDk76oTLm1XDtPSOJvys/pIsOlhUPHQGpuo7waHXvJJX51EwaZNH0WWPFcwmkFUUqBhGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:27:23.578033Z"},"content_sha256":"d1a29359e9aee73564ef3468fd102981cbce48c57eec7b904c90d4f9c54e661f","schema_version":"1.0","event_id":"sha256:d1a29359e9aee73564ef3468fd102981cbce48c57eec7b904c90d4f9c54e661f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZUYEUE6KVQETCBUPS6GOICB5Y/bundle.json","state_url":"https://pith.science/pith/NZUYEUE6KVQETCBUPS6GOICB5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZUYEUE6KVQETCBUPS6GOICB5Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T20:27:23Z","links":{"resolver":"https://pith.science/pith/NZUYEUE6KVQETCBUPS6GOICB5Y","bundle":"https://pith.science/pith/NZUYEUE6KVQETCBUPS6GOICB5Y/bundle.json","state":"https://pith.science/pith/NZUYEUE6KVQETCBUPS6GOICB5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZUYEUE6KVQETCBUPS6GOICB5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:NZUYEUE6KVQETCBUPS6GOICB5Y","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":"0db62244ebac137bbb562a243fb0b7c5961652f3e4a114bb2b492b9648e71e18","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2000-07-21T09:32:14Z","title_canon_sha256":"73dc09ffa917b04213bfc6dfb922b7899296986b0a4dcae489e6ea5eb16c939a"},"schema_version":"1.0","source":{"id":"quant-ph/0007081","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0007081","created_at":"2026-05-18T01:05:06Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0007081v3","created_at":"2026-05-18T01:05:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0007081","created_at":"2026-05-18T01:05:06Z"},{"alias_kind":"pith_short_12","alias_value":"NZUYEUE6KVQE","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"NZUYEUE6KVQETCBU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"NZUYEUE6","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:d1a29359e9aee73564ef3468fd102981cbce48c57eec7b904c90d4f9c54e661f","target":"graph","created_at":"2026-05-18T01:05:06Z","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 present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on the full state space and is shown to be an entanglement monotone, that is, it cannot increase under local quantum operations with classical communication and under mixing. For a large class of mixed states this measure of entanglement can be calculated exactly, and it provides a detailed classification of mixed states.","authors_text":"H.-J. Briegel, J. Eisert","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2000-07-21T09:32:14Z","title":"The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0007081","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:cb85a0a9944cece58a0dba65bd7cb7e9698f152fd423c4a4f2d510d3b7138e92","target":"record","created_at":"2026-05-18T01:05:06Z","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":"0db62244ebac137bbb562a243fb0b7c5961652f3e4a114bb2b492b9648e71e18","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2000-07-21T09:32:14Z","title_canon_sha256":"73dc09ffa917b04213bfc6dfb922b7899296986b0a4dcae489e6ea5eb16c939a"},"schema_version":"1.0","source":{"id":"quant-ph/0007081","kind":"arxiv","version":3}},"canonical_sha256":"6e6982509e55604988347cbc672041ee21a555040fb5ba741a724c5bcc4d19b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e6982509e55604988347cbc672041ee21a555040fb5ba741a724c5bcc4d19b5","first_computed_at":"2026-05-18T01:05:06.821125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:06.821125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aC/OGusDUc9E9oy3LMFqGKZ7zr+0dUINCBEME3dQG544M35VmA2CB4hM6nIp7c6kE0qIxKQhnhckLy3OHi7GBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:06.821770Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0007081","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb85a0a9944cece58a0dba65bd7cb7e9698f152fd423c4a4f2d510d3b7138e92","sha256:d1a29359e9aee73564ef3468fd102981cbce48c57eec7b904c90d4f9c54e661f"],"state_sha256":"629916c711f90fd63b3a421a6b8fb8951827e50e861074b8e899de6e8fc3c4a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wY6yPKO1DnC2hETvbWhkVoKik/74AKJfsHQf52ME2s2JEj2tO2/1WAxHq5X9GIvHmxLreRhNCo+feEOr4tX1Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:27:23.581749Z","bundle_sha256":"40db9d216509c19086e005159cd38ae54f1e8ab64c7b2196c1e31c6244a42875"}}