{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B5VDR32DWFLTQYYDB34R34KGZY","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":"084b7dcee8bbf5406d01a561fba1f046ca8ea301785015f161360c263af049db","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-03-09T17:14:09Z","title_canon_sha256":"40f324a8460316545bee03b380cc2f46d71c7653806670b3c77ab2a1bfd2256a"},"schema_version":"1.0","source":{"id":"1203.2142","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2142","created_at":"2026-05-18T02:21:17Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2142v2","created_at":"2026-05-18T02:21:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2142","created_at":"2026-05-18T02:21:17Z"},{"alias_kind":"pith_short_12","alias_value":"B5VDR32DWFLT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B5VDR32DWFLTQYYD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B5VDR32D","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:c4d9ae0669827828f68908b6dc2aebedc6e52b2f903e8ac55be03230e2eadf2b","target":"graph","created_at":"2026-05-18T02:21:17Z","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":"This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography.\n  We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\\'enyi entropies. We introduce the purified distance, a novel metric for unnormalized quantum states and use it to define smooth entropies as optimizations of the min- and max-entropies over a ball of close states. We explore various properties of these entropies, including data-processing inequalities, chain rules and their classical limits. The most important ","authors_text":"Marco Tomamichel","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-03-09T17:14:09Z","title":"A Framework for Non-Asymptotic Quantum Information Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2142","kind":"arxiv","version":2},"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":"sha256:93a296600c39ff293374c0ffbcebf96a2f678379f9a9e6869b4ceaec1f395839","target":"record","created_at":"2026-05-18T02:21:17Z","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":"084b7dcee8bbf5406d01a561fba1f046ca8ea301785015f161360c263af049db","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-03-09T17:14:09Z","title_canon_sha256":"40f324a8460316545bee03b380cc2f46d71c7653806670b3c77ab2a1bfd2256a"},"schema_version":"1.0","source":{"id":"1203.2142","kind":"arxiv","version":2}},"canonical_sha256":"0f6a38ef43b1573863030ef91df146ce1a3cdc155eb0f4297b4658e373103d24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f6a38ef43b1573863030ef91df146ce1a3cdc155eb0f4297b4658e373103d24","first_computed_at":"2026-05-18T02:21:17.158749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:17.158749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vhp5MBErOG4k6RdB3G1t/fZ6trrKWmOgZb6FD3VnBZthGYeUDHYaKYOgwXthJV6b1argSx4EHYMnbl/8SKeNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:17.159378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2142","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93a296600c39ff293374c0ffbcebf96a2f678379f9a9e6869b4ceaec1f395839","sha256:c4d9ae0669827828f68908b6dc2aebedc6e52b2f903e8ac55be03230e2eadf2b"],"state_sha256":"53078a02c9503aabe8556d6f82f0485195a308f7fd9ebfc32b8c5db5896814e6"}