{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5NBV7L3V3BRDRPIKLU5HLHQHD2","short_pith_number":"pith:5NBV7L3V","canonical_record":{"source":{"id":"1604.02783","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-11T03:56:11Z","cross_cats_sorted":[],"title_canon_sha256":"08ac318a7b5a4550f4ba916cd8999bf1a2ce27c519280c3badd09c200168216e","abstract_canon_sha256":"5bd302ba339f4afefd05353f75d2efe15df0a25affc6a23b25e1949334ac1159"},"schema_version":"1.0"},"canonical_sha256":"eb435faf75d86238bd0a5d3a759e071e96f7adf783a0e436a3dabaaa94504b41","source":{"kind":"arxiv","id":"1604.02783","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02783","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02783v3","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02783","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"pith_short_12","alias_value":"5NBV7L3V3BRD","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5NBV7L3V3BRDRPIK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5NBV7L3V","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5NBV7L3V3BRDRPIKLU5HLHQHD2","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02783","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-11T03:56:11Z","cross_cats_sorted":[],"title_canon_sha256":"08ac318a7b5a4550f4ba916cd8999bf1a2ce27c519280c3badd09c200168216e","abstract_canon_sha256":"5bd302ba339f4afefd05353f75d2efe15df0a25affc6a23b25e1949334ac1159"},"schema_version":"1.0"},"canonical_sha256":"eb435faf75d86238bd0a5d3a759e071e96f7adf783a0e436a3dabaaa94504b41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:34.598810Z","signature_b64":"X90RNZRiKVFMOhCDIoaOMw2CKSFfO4cr1aSHRSmx+jmhQf6KNZdzwmmlyvQv/rTerftIre3OyxtCBpynb9wHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb435faf75d86238bd0a5d3a759e071e96f7adf783a0e436a3dabaaa94504b41","last_reissued_at":"2026-05-18T00:49:34.598248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:34.598248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02783","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":"2026-05-18T00:49:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/k6+Oe8SJAX+C0aHn8JemMnbAFpAw/1VS6eDbELtK3CxIaL6HC153g8xwaUuHcKUM09urrKSSwHzdrpEipJ3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:18:58.564285Z"},"content_sha256":"96008bad1b177d8df53ea1cedef7917f097aab95ef432be15ca6da57f049047c","schema_version":"1.0","event_id":"sha256:96008bad1b177d8df53ea1cedef7917f097aab95ef432be15ca6da57f049047c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5NBV7L3V3BRDRPIKLU5HLHQHD2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower and upper bounds for entanglement of R\\'enyi-$\\alpha$ entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lin Chen, Wei Song, Zhuo-Liang Cao","submitted_at":"2016-04-11T03:56:11Z","abstract_excerpt":"Entanglement R\\'enyi-$\\alpha$ entropy is an entanglement measure. It generalizes the entanglement of formation, and they coincide when $\\alpha$ tends to 1. We derive analytical lower and upper bounds for the entanglement R\\'enyi-$\\alpha$ entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement R\\'enyi-$\\alpha$ entropy and some other entanglement measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02783","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":"2026-05-18T00:49:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8Qa48Xb2HT1lr3z60IIIRrMMLEMrzKD6b+FGH5ZivtMUdhJ7xWe7E231mTd5pdROISOemYiP+CuEQtUfTw0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:18:58.565079Z"},"content_sha256":"9b553f2a491f5e67e961d73901f9d7e83619c79777971f818f98dbfac3fb7f68","schema_version":"1.0","event_id":"sha256:9b553f2a491f5e67e961d73901f9d7e83619c79777971f818f98dbfac3fb7f68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NBV7L3V3BRDRPIKLU5HLHQHD2/bundle.json","state_url":"https://pith.science/pith/5NBV7L3V3BRDRPIKLU5HLHQHD2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NBV7L3V3BRDRPIKLU5HLHQHD2/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":"2026-05-31T13:18:58Z","links":{"resolver":"https://pith.science/pith/5NBV7L3V3BRDRPIKLU5HLHQHD2","bundle":"https://pith.science/pith/5NBV7L3V3BRDRPIKLU5HLHQHD2/bundle.json","state":"https://pith.science/pith/5NBV7L3V3BRDRPIKLU5HLHQHD2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NBV7L3V3BRDRPIKLU5HLHQHD2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5NBV7L3V3BRDRPIKLU5HLHQHD2","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":"5bd302ba339f4afefd05353f75d2efe15df0a25affc6a23b25e1949334ac1159","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-11T03:56:11Z","title_canon_sha256":"08ac318a7b5a4550f4ba916cd8999bf1a2ce27c519280c3badd09c200168216e"},"schema_version":"1.0","source":{"id":"1604.02783","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02783","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02783v3","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02783","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"pith_short_12","alias_value":"5NBV7L3V3BRD","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5NBV7L3V3BRDRPIK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5NBV7L3V","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:9b553f2a491f5e67e961d73901f9d7e83619c79777971f818f98dbfac3fb7f68","target":"graph","created_at":"2026-05-18T00:49:34Z","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":"Entanglement R\\'enyi-$\\alpha$ entropy is an entanglement measure. It generalizes the entanglement of formation, and they coincide when $\\alpha$ tends to 1. We derive analytical lower and upper bounds for the entanglement R\\'enyi-$\\alpha$ entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement R\\'enyi-$\\alpha$ entropy and some other entanglement measures.","authors_text":"Lin Chen, Wei Song, Zhuo-Liang Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-11T03:56:11Z","title":"Lower and upper bounds for entanglement of R\\'enyi-$\\alpha$ entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02783","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":"sha256:96008bad1b177d8df53ea1cedef7917f097aab95ef432be15ca6da57f049047c","target":"record","created_at":"2026-05-18T00:49:34Z","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":"5bd302ba339f4afefd05353f75d2efe15df0a25affc6a23b25e1949334ac1159","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-11T03:56:11Z","title_canon_sha256":"08ac318a7b5a4550f4ba916cd8999bf1a2ce27c519280c3badd09c200168216e"},"schema_version":"1.0","source":{"id":"1604.02783","kind":"arxiv","version":3}},"canonical_sha256":"eb435faf75d86238bd0a5d3a759e071e96f7adf783a0e436a3dabaaa94504b41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb435faf75d86238bd0a5d3a759e071e96f7adf783a0e436a3dabaaa94504b41","first_computed_at":"2026-05-18T00:49:34.598248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:34.598248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X90RNZRiKVFMOhCDIoaOMw2CKSFfO4cr1aSHRSmx+jmhQf6KNZdzwmmlyvQv/rTerftIre3OyxtCBpynb9wHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:34.598810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02783","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96008bad1b177d8df53ea1cedef7917f097aab95ef432be15ca6da57f049047c","sha256:9b553f2a491f5e67e961d73901f9d7e83619c79777971f818f98dbfac3fb7f68"],"state_sha256":"3397b937d8d1ee8c1faccf990564d2376f2465886a9bfeabb9235280687bc906"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KV4mHo+4mw/CRBPFNPOs0yR7+YmHq3A7zV9vHl55EijuXoev56YEH2QwZ+xPJeztsLRNOfmNaTK35DYUHgQ1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:18:58.569437Z","bundle_sha256":"7b8c9c3307e179b5a167c40bedca74609121f3cf84fe04ac8f4aa089f9513851"}}