{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HKDEM2R6VEST3GQXOWVLV5FM5Y","short_pith_number":"pith:HKDEM2R6","canonical_record":{"source":{"id":"2502.01611","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-03T18:44:59Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.OA"],"title_canon_sha256":"f2e0887651d76f7b9f4802545bf4a3442fd429086d6b7c914d08a7f3180fc3f4","abstract_canon_sha256":"b11e97edfe51b0418656e278aea9aec1d8959d99699161b7fbc1eab348a1cd9c"},"schema_version":"1.0"},"canonical_sha256":"3a86466a3ea9253d9a1775aabaf4acee0a80f501cadc81f3cca6bd78bc96d33a","source":{"kind":"arxiv","id":"2502.01611","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.01611","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"2502.01611v3","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01611","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"HKDEM2R6VEST","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"pith_short_16","alias_value":"HKDEM2R6VEST3GQX","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"pith_short_8","alias_value":"HKDEM2R6","created_at":"2026-06-11T01:09:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HKDEM2R6VEST3GQXOWVLV5FM5Y","target":"record","payload":{"canonical_record":{"source":{"id":"2502.01611","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-03T18:44:59Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.OA"],"title_canon_sha256":"f2e0887651d76f7b9f4802545bf4a3442fd429086d6b7c914d08a7f3180fc3f4","abstract_canon_sha256":"b11e97edfe51b0418656e278aea9aec1d8959d99699161b7fbc1eab348a1cd9c"},"schema_version":"1.0"},"canonical_sha256":"3a86466a3ea9253d9a1775aabaf4acee0a80f501cadc81f3cca6bd78bc96d33a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:09:11.221656Z","signature_b64":"lVNdLpbB9n+WRaAZrhbkZdA6330HGRFASgeIJpFGtFMpGjax8Leei6A1KW/ikQoS8I20b9XCsWfsg3EdtGU0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a86466a3ea9253d9a1775aabaf4acee0a80f501cadc81f3cca6bd78bc96d33a","last_reissued_at":"2026-06-11T01:09:11.220691Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:09:11.220691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.01611","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-11T01:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XZmmsediHMZr4u6MZW55udnrvuI/3t2kxLVjHQQEA2pbgPIf7fo7IKnAkV5zRUtgmv3ZcxSiQaFRKhzNjY4BBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:47:52.508749Z"},"content_sha256":"c29c51ea3a0fbfc50e345e7744b8c35976eb01d3d1445b1f2f5f5031e3ba051c","schema_version":"1.0","event_id":"sha256:c29c51ea3a0fbfc50e345e7744b8c35976eb01d3d1445b1f2f5f5031e3ba051c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HKDEM2R6VEST3GQXOWVLV5FM5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Additivity and chain rules for quantum entropies via multi-index Schatten norms","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Cambyse Rouz\\'e, Jan Kochanowski, Omar Fawzi, Thomas Van Himbeeck","submitted_at":"2025-02-03T18:44:59Z","abstract_excerpt":"The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often plays a crucial role. A fundamental question in quantum information and cryptography is whether the minimum output entropy remains additive under the tensor product of channels. Here, we establish a general additivity statement for the optimized sandwiched R\\'enyi entropy of quantum channels. For that, we generalize the results of [Devetak, Junge, King, Ruskai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01611","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.01611/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-11T01:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rSKm9wuXV66t0qP3xfS1F6AENGY/nRhXbTcgriCAIV3No5BtonYecfKHHuqs/jbd1pCTVuFD2U6a7dmx1Rn9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:47:52.509293Z"},"content_sha256":"5c22cfbf03ee2bfcd225ebd9de348ab56016da09c37e6f49812254ecf991877d","schema_version":"1.0","event_id":"sha256:5c22cfbf03ee2bfcd225ebd9de348ab56016da09c37e6f49812254ecf991877d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKDEM2R6VEST3GQXOWVLV5FM5Y/bundle.json","state_url":"https://pith.science/pith/HKDEM2R6VEST3GQXOWVLV5FM5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKDEM2R6VEST3GQXOWVLV5FM5Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-06T11:47:52Z","links":{"resolver":"https://pith.science/pith/HKDEM2R6VEST3GQXOWVLV5FM5Y","bundle":"https://pith.science/pith/HKDEM2R6VEST3GQXOWVLV5FM5Y/bundle.json","state":"https://pith.science/pith/HKDEM2R6VEST3GQXOWVLV5FM5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKDEM2R6VEST3GQXOWVLV5FM5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HKDEM2R6VEST3GQXOWVLV5FM5Y","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":"b11e97edfe51b0418656e278aea9aec1d8959d99699161b7fbc1eab348a1cd9c","cross_cats_sorted":["math-ph","math.FA","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-03T18:44:59Z","title_canon_sha256":"f2e0887651d76f7b9f4802545bf4a3442fd429086d6b7c914d08a7f3180fc3f4"},"schema_version":"1.0","source":{"id":"2502.01611","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.01611","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"2502.01611v3","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01611","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"HKDEM2R6VEST","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"pith_short_16","alias_value":"HKDEM2R6VEST3GQX","created_at":"2026-06-11T01:09:11Z"},{"alias_kind":"pith_short_8","alias_value":"HKDEM2R6","created_at":"2026-06-11T01:09:11Z"}],"graph_snapshots":[{"event_id":"sha256:5c22cfbf03ee2bfcd225ebd9de348ab56016da09c37e6f49812254ecf991877d","target":"graph","created_at":"2026-06-11T01:09:11Z","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/2502.01611/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often plays a crucial role. A fundamental question in quantum information and cryptography is whether the minimum output entropy remains additive under the tensor product of channels. Here, we establish a general additivity statement for the optimized sandwiched R\\'enyi entropy of quantum channels. For that, we generalize the results of [Devetak, Junge, King, Ruskai","authors_text":"Cambyse Rouz\\'e, Jan Kochanowski, Omar Fawzi, Thomas Van Himbeeck","cross_cats":["math-ph","math.FA","math.MP","math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-03T18:44:59Z","title":"Additivity and chain rules for quantum entropies via multi-index Schatten norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01611","kind":"arxiv","version":3},"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:c29c51ea3a0fbfc50e345e7744b8c35976eb01d3d1445b1f2f5f5031e3ba051c","target":"record","created_at":"2026-06-11T01:09:11Z","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":"b11e97edfe51b0418656e278aea9aec1d8959d99699161b7fbc1eab348a1cd9c","cross_cats_sorted":["math-ph","math.FA","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-03T18:44:59Z","title_canon_sha256":"f2e0887651d76f7b9f4802545bf4a3442fd429086d6b7c914d08a7f3180fc3f4"},"schema_version":"1.0","source":{"id":"2502.01611","kind":"arxiv","version":3}},"canonical_sha256":"3a86466a3ea9253d9a1775aabaf4acee0a80f501cadc81f3cca6bd78bc96d33a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a86466a3ea9253d9a1775aabaf4acee0a80f501cadc81f3cca6bd78bc96d33a","first_computed_at":"2026-06-11T01:09:11.220691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:09:11.220691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lVNdLpbB9n+WRaAZrhbkZdA6330HGRFASgeIJpFGtFMpGjax8Leei6A1KW/ikQoS8I20b9XCsWfsg3EdtGU0DA==","signature_status":"signed_v1","signed_at":"2026-06-11T01:09:11.221656Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.01611","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c29c51ea3a0fbfc50e345e7744b8c35976eb01d3d1445b1f2f5f5031e3ba051c","sha256:5c22cfbf03ee2bfcd225ebd9de348ab56016da09c37e6f49812254ecf991877d"],"state_sha256":"86cd734fd0cac21f5bcc4ef2fcb8a68127c8b3c4ff16dfdd3e5f90d15b1204b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0BBs8kotvuUTMYdyqk9oSTo/ODSyJ97oXW6qB5i8e8oC+eLA3mtKc1BMxn3O3VjvwbCOMPXqxXvNMuD5xqFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T11:47:52.512547Z","bundle_sha256":"88ce718705d0b0f943fa5eaba11bf516da2ec7d223bda6b6440b6cebf83ae960"}}