{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2VH4QICTZM2GN2ENJF5YYDA3J7","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":"1fa3bd900e79ede28e57eeabaa068bd6399c512a0094a87b052ab02d6cbe17d0","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-11T04:00:54Z","title_canon_sha256":"3ac995dfd3c658cb6709d99bb35780d730d3b64299fb25a9c48376d2ec13cea8"},"schema_version":"1.0","source":{"id":"1608.03362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03362","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03362v2","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03362","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"2VH4QICTZM2G","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2VH4QICTZM2GN2EN","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2VH4QICT","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:ebda9ee34ecef8e7089c700cdc61f1a9f7e14fa28a11784b2bbc4a4cdd4dfdd4","target":"graph","created_at":"2026-05-18T01:04:02Z","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":"The R{\\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital importance. Another important quantity is R{\\'e}nyi relative entropy on which R{\\'e}nyi generalization of the conditional entropy, and mutual information are defined based. Thus, finding lower bound for R{\\'e}nyi relative entropy is our goal in this paper. We use matrix inequalities to prove new bounds on the entropy of type $\\beta$, R{\\'e}nyi entropy.","authors_text":"Hadi Reisizadeh, S. Mahmoud Manjegani","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-11T04:00:54Z","title":"Some applications of matrix inequalities in R\\'enyi entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03362","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":"sha256:809e32f5f6081ac1895e087d6f3a5c9819cb8806ac8e4a906a22ac60b85718b0","target":"record","created_at":"2026-05-18T01:04:02Z","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":"1fa3bd900e79ede28e57eeabaa068bd6399c512a0094a87b052ab02d6cbe17d0","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-11T04:00:54Z","title_canon_sha256":"3ac995dfd3c658cb6709d99bb35780d730d3b64299fb25a9c48376d2ec13cea8"},"schema_version":"1.0","source":{"id":"1608.03362","kind":"arxiv","version":2}},"canonical_sha256":"d54fc82053cb3466e88d497b8c0c1b4fd1d250a14989aa644ec3f83d5e353ccf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d54fc82053cb3466e88d497b8c0c1b4fd1d250a14989aa644ec3f83d5e353ccf","first_computed_at":"2026-05-18T01:04:02.303216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:02.303216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/rKQ+L5cdSTPprAfdMkr/L0dm/RH4LsbQ/KUlZNC9SDCLiuvn+H2sJ2JLx3JWucaHBbLI/h/kTWrA7tk7q75Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:02.303719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:809e32f5f6081ac1895e087d6f3a5c9819cb8806ac8e4a906a22ac60b85718b0","sha256:ebda9ee34ecef8e7089c700cdc61f1a9f7e14fa28a11784b2bbc4a4cdd4dfdd4"],"state_sha256":"b520dbc228df212585a8f35b35e417112718a93bbec08a607c04a5a7dcac73c0"}