{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HAP5MVMV6I3UVTAGJK4VJABIHP","short_pith_number":"pith:HAP5MVMV","schema_version":"1.0","canonical_sha256":"381fd65595f2374acc064ab95480283be34b073fd27c9b3e5a20d37b6b1e0a27","source":{"kind":"arxiv","id":"1604.03089","version":4},"attestation_state":"computed","paper":{"title":"Different quantum f-divergences and the reversibility of quantum operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Fumio Hiai, Milan Mosonyi","submitted_at":"2016-04-11T19:53:37Z","abstract_excerpt":"The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the R\\'enyi divergences. Various quantum versions of this concept, and more narrowly, the concept of R\\'enyi divergences, have been introduced in the literature with applications in quantum information theory; most notably Petz' quasi-entropies (standard $f$-divergences), Matsumoto's maximal $f$-divergences, measured $f$-divergences, and sandwiched and $\\alpha$-$z$-R\\'enyi divergences.\n  In this paper we"},"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":"1604.03089","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-11T19:53:37Z","cross_cats_sorted":["cs.IT","math.IT","math.MP","quant-ph"],"title_canon_sha256":"0dcb866e9306fff4bef69dd333f8da953308effd3be711503173cdf758dc0cce","abstract_canon_sha256":"2cb9b551694bd7703e36af1294971e52eea94faefc71590568f118a72021d480"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:36.534079Z","signature_b64":"ucNG1SvmnnFutzDzBNILGgppdIiFYVAhEUPrHfkJ3IWn/h2UB0+uMkitMcqSNd/vT9ksRKl2TfhLvfipMqwsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"381fd65595f2374acc064ab95480283be34b073fd27c9b3e5a20d37b6b1e0a27","last_reissued_at":"2026-05-18T00:38:36.533595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:36.533595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Different quantum f-divergences and the reversibility of quantum operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Fumio Hiai, Milan Mosonyi","submitted_at":"2016-04-11T19:53:37Z","abstract_excerpt":"The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the R\\'enyi divergences. Various quantum versions of this concept, and more narrowly, the concept of R\\'enyi divergences, have been introduced in the literature with applications in quantum information theory; most notably Petz' quasi-entropies (standard $f$-divergences), Matsumoto's maximal $f$-divergences, measured $f$-divergences, and sandwiched and $\\alpha$-$z$-R\\'enyi divergences.\n  In this paper we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03089","kind":"arxiv","version":4},"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":"1604.03089","created_at":"2026-05-18T00:38:36.533669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.03089v4","created_at":"2026-05-18T00:38:36.533669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03089","created_at":"2026-05-18T00:38:36.533669+00:00"},{"alias_kind":"pith_short_12","alias_value":"HAP5MVMV6I3U","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HAP5MVMV6I3UVTAG","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HAP5MVMV","created_at":"2026-05-18T12:30:19.053100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2402.18500","citing_title":"Conditional Independence of 1D Gibbs States with Applications to Efficient Learning","ref_index":44,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HAP5MVMV6I3UVTAGJK4VJABIHP","json":"https://pith.science/pith/HAP5MVMV6I3UVTAGJK4VJABIHP.json","graph_json":"https://pith.science/api/pith-number/HAP5MVMV6I3UVTAGJK4VJABIHP/graph.json","events_json":"https://pith.science/api/pith-number/HAP5MVMV6I3UVTAGJK4VJABIHP/events.json","paper":"https://pith.science/paper/HAP5MVMV"},"agent_actions":{"view_html":"https://pith.science/pith/HAP5MVMV6I3UVTAGJK4VJABIHP","download_json":"https://pith.science/pith/HAP5MVMV6I3UVTAGJK4VJABIHP.json","view_paper":"https://pith.science/paper/HAP5MVMV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.03089&json=true","fetch_graph":"https://pith.science/api/pith-number/HAP5MVMV6I3UVTAGJK4VJABIHP/graph.json","fetch_events":"https://pith.science/api/pith-number/HAP5MVMV6I3UVTAGJK4VJABIHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HAP5MVMV6I3UVTAGJK4VJABIHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HAP5MVMV6I3UVTAGJK4VJABIHP/action/storage_attestation","attest_author":"https://pith.science/pith/HAP5MVMV6I3UVTAGJK4VJABIHP/action/author_attestation","sign_citation":"https://pith.science/pith/HAP5MVMV6I3UVTAGJK4VJABIHP/action/citation_signature","submit_replication":"https://pith.science/pith/HAP5MVMV6I3UVTAGJK4VJABIHP/action/replication_record"}},"created_at":"2026-05-18T00:38:36.533669+00:00","updated_at":"2026-05-18T00:38:36.533669+00:00"}