{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GJRQUTBMA7YZIPNX6YJHNCSUR7","short_pith_number":"pith:GJRQUTBM","canonical_record":{"source":{"id":"1010.1920","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-10T13:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"a935ec73df1feb1dad2407cfa4db5a09aba3650f01d80918a1f3fd04ec303b9b","abstract_canon_sha256":"7e8ac76111027cfd4ac42ed1f5cc50d9b1abeaf39243c77bb3cf78467903d196"},"schema_version":"1.0"},"canonical_sha256":"32630a4c2c07f1943db7f612768a548fcbffa20394f9d3fa8de87f769f20fcc8","source":{"kind":"arxiv","id":"1010.1920","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1920","created_at":"2026-05-18T02:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1920v3","created_at":"2026-05-18T02:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1920","created_at":"2026-05-18T02:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"GJRQUTBMA7YZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GJRQUTBMA7YZIPNX","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GJRQUTBM","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GJRQUTBMA7YZIPNX6YJHNCSUR7","target":"record","payload":{"canonical_record":{"source":{"id":"1010.1920","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-10T13:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"a935ec73df1feb1dad2407cfa4db5a09aba3650f01d80918a1f3fd04ec303b9b","abstract_canon_sha256":"7e8ac76111027cfd4ac42ed1f5cc50d9b1abeaf39243c77bb3cf78467903d196"},"schema_version":"1.0"},"canonical_sha256":"32630a4c2c07f1943db7f612768a548fcbffa20394f9d3fa8de87f769f20fcc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:07.118150Z","signature_b64":"Q5+phsEHItVVfnETKJhsbpj2QYzI7GDDL/uEt/941FVtwjREQaXMdwJbtBaZD/U7NgLJJbJgxpIW0UB2+rfSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32630a4c2c07f1943db7f612768a548fcbffa20394f9d3fa8de87f769f20fcc8","last_reissued_at":"2026-05-18T02:05:07.117295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:07.117295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.1920","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":"2026-05-18T02:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZaqdERluo0GN+Z9Rc4tIPy1iON0SD1FhL5Tp/l29TxzvmRrpiFaVVp/yLxTDIYx9dWSGFxEyVjRfHb4lg/IDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:42:32.957734Z"},"content_sha256":"40112f1795240b31eaeab0fc2106b62c8a3143ea2a39a8bac292d33ae1de6d05","schema_version":"1.0","event_id":"sha256:40112f1795240b31eaeab0fc2106b62c8a3143ea2a39a8bac292d33ae1de6d05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GJRQUTBMA7YZIPNX6YJHNCSUR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight lower bound to the geometric measure of quantum discord","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Ali Saif M. Hassan, Behzad Lari, Pramod S. Joag","submitted_at":"2010-10-10T13:21:48Z","abstract_excerpt":"Dakic, Vedral and Brukner [Physical Review Letters \\tf{105},190502 (2010)] gave a geometric measure of quantum discord in a bipartite quantum state as the distance of the state from the closest classical quantum (or zero discord) state and derived an explicit formula for a two qubit state. Further, S.Luo and S.Fu [Physical Review A \\tf{82}, 034302 (2010)] obtained a generic form of this geometric measure for a general bipartite state and established a lower bound. In this brief report we obtain a rigorous lower bound to the geometric measure of quantum discord in a general bipartite state whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1920","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":"2026-05-18T02:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1WTVhqtNL6g2/VO+S1BlAx22BGJKpeepmlNYfataOWFqbEfmKKoBRKYJ3hngsiLn00y6a9sySisLbu91rVmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:42:32.958071Z"},"content_sha256":"9054f6e9c6e98fe8bae0f7fcf413638b8dd6ce6424c443689bfe0c260d513aef","schema_version":"1.0","event_id":"sha256:9054f6e9c6e98fe8bae0f7fcf413638b8dd6ce6424c443689bfe0c260d513aef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJRQUTBMA7YZIPNX6YJHNCSUR7/bundle.json","state_url":"https://pith.science/pith/GJRQUTBMA7YZIPNX6YJHNCSUR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJRQUTBMA7YZIPNX6YJHNCSUR7/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":"2026-06-30T06:42:32Z","links":{"resolver":"https://pith.science/pith/GJRQUTBMA7YZIPNX6YJHNCSUR7","bundle":"https://pith.science/pith/GJRQUTBMA7YZIPNX6YJHNCSUR7/bundle.json","state":"https://pith.science/pith/GJRQUTBMA7YZIPNX6YJHNCSUR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJRQUTBMA7YZIPNX6YJHNCSUR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GJRQUTBMA7YZIPNX6YJHNCSUR7","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":"7e8ac76111027cfd4ac42ed1f5cc50d9b1abeaf39243c77bb3cf78467903d196","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-10T13:21:48Z","title_canon_sha256":"a935ec73df1feb1dad2407cfa4db5a09aba3650f01d80918a1f3fd04ec303b9b"},"schema_version":"1.0","source":{"id":"1010.1920","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1920","created_at":"2026-05-18T02:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1920v3","created_at":"2026-05-18T02:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1920","created_at":"2026-05-18T02:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"GJRQUTBMA7YZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GJRQUTBMA7YZIPNX","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GJRQUTBM","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:9054f6e9c6e98fe8bae0f7fcf413638b8dd6ce6424c443689bfe0c260d513aef","target":"graph","created_at":"2026-05-18T02:05:07Z","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":"Dakic, Vedral and Brukner [Physical Review Letters \\tf{105},190502 (2010)] gave a geometric measure of quantum discord in a bipartite quantum state as the distance of the state from the closest classical quantum (or zero discord) state and derived an explicit formula for a two qubit state. Further, S.Luo and S.Fu [Physical Review A \\tf{82}, 034302 (2010)] obtained a generic form of this geometric measure for a general bipartite state and established a lower bound. In this brief report we obtain a rigorous lower bound to the geometric measure of quantum discord in a general bipartite state whic","authors_text":"Ali Saif M. Hassan, Behzad Lari, Pramod S. Joag","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-10T13:21:48Z","title":"Tight lower bound to the geometric measure of quantum discord"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1920","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":"sha256:40112f1795240b31eaeab0fc2106b62c8a3143ea2a39a8bac292d33ae1de6d05","target":"record","created_at":"2026-05-18T02:05:07Z","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":"7e8ac76111027cfd4ac42ed1f5cc50d9b1abeaf39243c77bb3cf78467903d196","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-10T13:21:48Z","title_canon_sha256":"a935ec73df1feb1dad2407cfa4db5a09aba3650f01d80918a1f3fd04ec303b9b"},"schema_version":"1.0","source":{"id":"1010.1920","kind":"arxiv","version":3}},"canonical_sha256":"32630a4c2c07f1943db7f612768a548fcbffa20394f9d3fa8de87f769f20fcc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32630a4c2c07f1943db7f612768a548fcbffa20394f9d3fa8de87f769f20fcc8","first_computed_at":"2026-05-18T02:05:07.117295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:07.117295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q5+phsEHItVVfnETKJhsbpj2QYzI7GDDL/uEt/941FVtwjREQaXMdwJbtBaZD/U7NgLJJbJgxpIW0UB2+rfSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:07.118150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1920","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40112f1795240b31eaeab0fc2106b62c8a3143ea2a39a8bac292d33ae1de6d05","sha256:9054f6e9c6e98fe8bae0f7fcf413638b8dd6ce6424c443689bfe0c260d513aef"],"state_sha256":"fef815482ed256f132ffe13325ba04064aa0bf0aef6def991d3dfe9a0ad37e89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqIjrUYNmQ/PvxgAWhdgYzpqJpzUkEhBss2UTSXg8WzvNH1/nLmTs+xb44vSbRUe2WeROjQOLEQNZ1I9/+GHCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T06:42:32.960055Z","bundle_sha256":"163cdc40ef8fc9e2c9ab2ec543e500e74ab68da7f6a59de2c2f514b86de166e0"}}