{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VII6TVSNZILRF6AL5E5ZUC7R5I","short_pith_number":"pith:VII6TVSN","schema_version":"1.0","canonical_sha256":"aa11e9d64dca1712f80be93b9a0bf1ea1a2c3dc900704aa28daaa6b83413f54a","source":{"kind":"arxiv","id":"1703.06149","version":2},"attestation_state":"computed","paper":{"title":"From log-determinant inequalities to Gaussian entanglement via recoverability theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andreas Winter, Christoph Hirche, Gerardo Adesso, Ludovico Lami","submitted_at":"2017-03-17T18:04:46Z","abstract_excerpt":"Many determinantal inequalities for positive definite block matrices are consequences of general entropy inequalities, specialised to Gaussian distributed vectors with prescribed covariances. In particular, strong subadditivity (SSA) yields \\begin{equation*} \\ln\\det V_{AC} + \\ln\\det V_{BC} - \\ln\\det V_{ABC} - \\ln\\det V_C \\geq 0 \\end{equation*} for all $3\\times 3$-block matrices $V_{ABC}$, where subscripts identify principal submatrices. We shall refer to the above inequality as SSA of log-det entropy. In this paper we develop further insights on the properties of the above inequality and its a"},"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":"1703.06149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-03-17T18:04:46Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4ae8257d2eec00ea8ebbaef8e982adf1f407abebe633232fa53669283d968bf9","abstract_canon_sha256":"8d1bd341dee9f2ef27abed419c548db7d02bf9304f61fe62ee2e279f01490542"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:23.824531Z","signature_b64":"g6JNlMQRp2Q+F06c2Ls0D6F6Iv9ws4DNrcQMMwwYdiEGurDPGKVuK0Z2CHq0Opp64XVxK7C7YVtcZf7GBqdIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa11e9d64dca1712f80be93b9a0bf1ea1a2c3dc900704aa28daaa6b83413f54a","last_reissued_at":"2026-05-18T00:31:23.824025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:23.824025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From log-determinant inequalities to Gaussian entanglement via recoverability theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andreas Winter, Christoph Hirche, Gerardo Adesso, Ludovico Lami","submitted_at":"2017-03-17T18:04:46Z","abstract_excerpt":"Many determinantal inequalities for positive definite block matrices are consequences of general entropy inequalities, specialised to Gaussian distributed vectors with prescribed covariances. In particular, strong subadditivity (SSA) yields \\begin{equation*} \\ln\\det V_{AC} + \\ln\\det V_{BC} - \\ln\\det V_{ABC} - \\ln\\det V_C \\geq 0 \\end{equation*} for all $3\\times 3$-block matrices $V_{ABC}$, where subscripts identify principal submatrices. We shall refer to the above inequality as SSA of log-det entropy. In this paper we develop further insights on the properties of the above inequality and its a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06149","kind":"arxiv","version":2},"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":"1703.06149","created_at":"2026-05-18T00:31:23.824103+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.06149v2","created_at":"2026-05-18T00:31:23.824103+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06149","created_at":"2026-05-18T00:31:23.824103+00:00"},{"alias_kind":"pith_short_12","alias_value":"VII6TVSNZILR","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VII6TVSNZILRF6AL","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VII6TVSN","created_at":"2026-05-18T12:31:49.984773+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/VII6TVSNZILRF6AL5E5ZUC7R5I","json":"https://pith.science/pith/VII6TVSNZILRF6AL5E5ZUC7R5I.json","graph_json":"https://pith.science/api/pith-number/VII6TVSNZILRF6AL5E5ZUC7R5I/graph.json","events_json":"https://pith.science/api/pith-number/VII6TVSNZILRF6AL5E5ZUC7R5I/events.json","paper":"https://pith.science/paper/VII6TVSN"},"agent_actions":{"view_html":"https://pith.science/pith/VII6TVSNZILRF6AL5E5ZUC7R5I","download_json":"https://pith.science/pith/VII6TVSNZILRF6AL5E5ZUC7R5I.json","view_paper":"https://pith.science/paper/VII6TVSN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.06149&json=true","fetch_graph":"https://pith.science/api/pith-number/VII6TVSNZILRF6AL5E5ZUC7R5I/graph.json","fetch_events":"https://pith.science/api/pith-number/VII6TVSNZILRF6AL5E5ZUC7R5I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VII6TVSNZILRF6AL5E5ZUC7R5I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VII6TVSNZILRF6AL5E5ZUC7R5I/action/storage_attestation","attest_author":"https://pith.science/pith/VII6TVSNZILRF6AL5E5ZUC7R5I/action/author_attestation","sign_citation":"https://pith.science/pith/VII6TVSNZILRF6AL5E5ZUC7R5I/action/citation_signature","submit_replication":"https://pith.science/pith/VII6TVSNZILRF6AL5E5ZUC7R5I/action/replication_record"}},"created_at":"2026-05-18T00:31:23.824103+00:00","updated_at":"2026-05-18T00:31:23.824103+00:00"}