{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3BBTKD7FWPNXNM3XXDS6IIZ2CH","short_pith_number":"pith:3BBTKD7F","schema_version":"1.0","canonical_sha256":"d843350fe5b3db76b377b8e5e4233a11e6d91a888048dd13edb0a45232c668c9","source":{"kind":"arxiv","id":"1302.7034","version":3},"attestation_state":"computed","paper":{"title":"Geometric quantum discord through the Schatten 1-norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"F. M. Paula, M. S. Sarandy, Thiago. R. de Oliveira","submitted_at":"2013-02-27T23:51:38Z","abstract_excerpt":"It has recently been pointed out that the geometric quantum discord, as defined by the Hilbert-Schmidt norm (2-norm), is not a good measure of quantum correlations, since it may increase under local reversible operations on the unmeasured subsystem. Here, we revisit the geometric discord by considering general Schatten p-norms, explicitly showing that the 1-norm is the only p-norm able to define a consistent quantum correlation measure. In addition, by restricting the optimization to the tetrahedron of two-qubit Bell-diagonal states, we provide an analytical expression for the 1-norm geometric"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.7034","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-27T23:51:38Z","cross_cats_sorted":[],"title_canon_sha256":"27e9f8a3d7f46ff8e029d2a9c8f1a5a90beabd9c85698c32af62dbba9fec5292","abstract_canon_sha256":"0fd294e14452ade88f245ba3a7002389117e066fcc6ea7f641e26d989f152df8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:23.615602Z","signature_b64":"65e5N2cMt5XlxUXbjKfgURLjatj/uQeEoDyNvAVm/HED8RL/sddy/Maez/zqcOuZDx86OsUutUtWAJE76g4ACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d843350fe5b3db76b377b8e5e4233a11e6d91a888048dd13edb0a45232c668c9","last_reissued_at":"2026-05-18T03:21:23.615093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:23.615093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric quantum discord through the Schatten 1-norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"F. M. Paula, M. S. Sarandy, Thiago. R. de Oliveira","submitted_at":"2013-02-27T23:51:38Z","abstract_excerpt":"It has recently been pointed out that the geometric quantum discord, as defined by the Hilbert-Schmidt norm (2-norm), is not a good measure of quantum correlations, since it may increase under local reversible operations on the unmeasured subsystem. Here, we revisit the geometric discord by considering general Schatten p-norms, explicitly showing that the 1-norm is the only p-norm able to define a consistent quantum correlation measure. In addition, by restricting the optimization to the tetrahedron of two-qubit Bell-diagonal states, we provide an analytical expression for the 1-norm geometric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7034","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1302.7034","created_at":"2026-05-18T03:21:23.615167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.7034v3","created_at":"2026-05-18T03:21:23.615167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7034","created_at":"2026-05-18T03:21:23.615167+00:00"},{"alias_kind":"pith_short_12","alias_value":"3BBTKD7FWPNX","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3BBTKD7FWPNXNM3X","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3BBTKD7F","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3BBTKD7FWPNXNM3XXDS6IIZ2CH","json":"https://pith.science/pith/3BBTKD7FWPNXNM3XXDS6IIZ2CH.json","graph_json":"https://pith.science/api/pith-number/3BBTKD7FWPNXNM3XXDS6IIZ2CH/graph.json","events_json":"https://pith.science/api/pith-number/3BBTKD7FWPNXNM3XXDS6IIZ2CH/events.json","paper":"https://pith.science/paper/3BBTKD7F"},"agent_actions":{"view_html":"https://pith.science/pith/3BBTKD7FWPNXNM3XXDS6IIZ2CH","download_json":"https://pith.science/pith/3BBTKD7FWPNXNM3XXDS6IIZ2CH.json","view_paper":"https://pith.science/paper/3BBTKD7F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.7034&json=true","fetch_graph":"https://pith.science/api/pith-number/3BBTKD7FWPNXNM3XXDS6IIZ2CH/graph.json","fetch_events":"https://pith.science/api/pith-number/3BBTKD7FWPNXNM3XXDS6IIZ2CH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3BBTKD7FWPNXNM3XXDS6IIZ2CH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3BBTKD7FWPNXNM3XXDS6IIZ2CH/action/storage_attestation","attest_author":"https://pith.science/pith/3BBTKD7FWPNXNM3XXDS6IIZ2CH/action/author_attestation","sign_citation":"https://pith.science/pith/3BBTKD7FWPNXNM3XXDS6IIZ2CH/action/citation_signature","submit_replication":"https://pith.science/pith/3BBTKD7FWPNXNM3XXDS6IIZ2CH/action/replication_record"}},"created_at":"2026-05-18T03:21:23.615167+00:00","updated_at":"2026-05-18T03:21:23.615167+00:00"}