{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:62YA7BTKVKNQSFZCLULPX237GY","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":"8cab6e61380802171a8cb80d55e45c66d5bcf34c08ee30534afc602993f57104","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-26T13:23:57Z","title_canon_sha256":"65b0007895da033468f96cd996777ce93eeef9906a76a35703878246f3fbb413"},"schema_version":"1.0","source":{"id":"1004.4519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4519","created_at":"2026-07-05T03:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4519v2","created_at":"2026-07-05T03:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4519","created_at":"2026-07-05T03:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"62YA7BTKVKNQ","created_at":"2026-07-05T03:34:03Z"},{"alias_kind":"pith_short_16","alias_value":"62YA7BTKVKNQSFZC","created_at":"2026-07-05T03:34:03Z"},{"alias_kind":"pith_short_8","alias_value":"62YA7BTK","created_at":"2026-07-05T03:34:03Z"}],"graph_snapshots":[{"event_id":"sha256:a55ec0c86c518e4b93144cb18e63475588611f265317110ba3e01ca8850ce18a","target":"graph","created_at":"2026-07-05T03:34:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1004.4519/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the infinite-dimensional case. The properties of the conditional entropy such as monotonicity, concavity and subadditivity are also generalized to the infinite-dimensional case.","authors_text":"A. A. Kuznetsova","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-26T13:23:57Z","title":"Quantum conditional entropy for infinite-dimensional systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4519","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":"sha256:679c390a51618a8206b3c8dc40f2555be805ddf63f70895da00e0b597dd762ac","target":"record","created_at":"2026-07-05T03:34:03Z","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":"8cab6e61380802171a8cb80d55e45c66d5bcf34c08ee30534afc602993f57104","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-26T13:23:57Z","title_canon_sha256":"65b0007895da033468f96cd996777ce93eeef9906a76a35703878246f3fbb413"},"schema_version":"1.0","source":{"id":"1004.4519","kind":"arxiv","version":2}},"canonical_sha256":"f6b00f866aaa9b0917225d16fbeb7f36182d3dba0c667c41a42e4266f1bf4ede","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6b00f866aaa9b0917225d16fbeb7f36182d3dba0c667c41a42e4266f1bf4ede","first_computed_at":"2026-07-05T03:34:03.694923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:34:03.694923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eky+4dNLonrepmKrldy2eVJK4E37aR3WeQc+ugFhODp+6TCkAXv4jWNHJ/K/Yg5L6dXh0QtdTO/zX2Jp38LeAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:34:03.695406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.4519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:679c390a51618a8206b3c8dc40f2555be805ddf63f70895da00e0b597dd762ac","sha256:a55ec0c86c518e4b93144cb18e63475588611f265317110ba3e01ca8850ce18a"],"state_sha256":"9d615d06fc8d85d6dd45dc2c502b3fc4c56e08adf6d72cd60294a9538725657f"}