{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:H2CU4MORUV2A4ICLWK6LUQ5QYE","short_pith_number":"pith:H2CU4MOR","schema_version":"1.0","canonical_sha256":"3e854e31d1a5740e204bb2bcba43b0c1303dec7146f8abb0aed0d74fa6b933e0","source":{"kind":"arxiv","id":"1507.00303","version":3},"attestation_state":"computed","paper":{"title":"Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Aram W. Harrow, David Sutter, Marco Tomamichel","submitted_at":"2015-07-01T18:05:39Z","abstract_excerpt":"The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a \"recovery map\" that exactly reverses the effects of the quantum channel on both states. In this paper we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination "},"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":"1507.00303","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-01T18:05:39Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7fe2cf5627194a6aed5abd9b7e2d86a49f4e006cd6e5bad86acdc7e05972acf5","abstract_canon_sha256":"3694418476d3a3253d669d1b28f929bdae98d93fcfbce724db4016621934e31c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:58.516413Z","signature_b64":"ZGeEAhMFUywO6LzGOwLSR66+COwGS2F6W504QtszngJsv/ir20eNVEPCFYCQPwRDsEvS3USGsAcvD+ISE6MjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e854e31d1a5740e204bb2bcba43b0c1303dec7146f8abb0aed0d74fa6b933e0","last_reissued_at":"2026-05-18T01:15:58.515735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:58.515735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Aram W. Harrow, David Sutter, Marco Tomamichel","submitted_at":"2015-07-01T18:05:39Z","abstract_excerpt":"The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a \"recovery map\" that exactly reverses the effects of the quantum channel on both states. In this paper we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00303","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":"1507.00303","created_at":"2026-05-18T01:15:58.515836+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.00303v3","created_at":"2026-05-18T01:15:58.515836+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00303","created_at":"2026-05-18T01:15:58.515836+00:00"},{"alias_kind":"pith_short_12","alias_value":"H2CU4MORUV2A","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"H2CU4MORUV2A4ICL","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"H2CU4MOR","created_at":"2026-05-18T12:29:22.688609+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/H2CU4MORUV2A4ICLWK6LUQ5QYE","json":"https://pith.science/pith/H2CU4MORUV2A4ICLWK6LUQ5QYE.json","graph_json":"https://pith.science/api/pith-number/H2CU4MORUV2A4ICLWK6LUQ5QYE/graph.json","events_json":"https://pith.science/api/pith-number/H2CU4MORUV2A4ICLWK6LUQ5QYE/events.json","paper":"https://pith.science/paper/H2CU4MOR"},"agent_actions":{"view_html":"https://pith.science/pith/H2CU4MORUV2A4ICLWK6LUQ5QYE","download_json":"https://pith.science/pith/H2CU4MORUV2A4ICLWK6LUQ5QYE.json","view_paper":"https://pith.science/paper/H2CU4MOR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.00303&json=true","fetch_graph":"https://pith.science/api/pith-number/H2CU4MORUV2A4ICLWK6LUQ5QYE/graph.json","fetch_events":"https://pith.science/api/pith-number/H2CU4MORUV2A4ICLWK6LUQ5QYE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H2CU4MORUV2A4ICLWK6LUQ5QYE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H2CU4MORUV2A4ICLWK6LUQ5QYE/action/storage_attestation","attest_author":"https://pith.science/pith/H2CU4MORUV2A4ICLWK6LUQ5QYE/action/author_attestation","sign_citation":"https://pith.science/pith/H2CU4MORUV2A4ICLWK6LUQ5QYE/action/citation_signature","submit_replication":"https://pith.science/pith/H2CU4MORUV2A4ICLWK6LUQ5QYE/action/replication_record"}},"created_at":"2026-05-18T01:15:58.515836+00:00","updated_at":"2026-05-18T01:15:58.515836+00:00"}