{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7QDDDMGCCGV77WMJHLJEKULWII","short_pith_number":"pith:7QDDDMGC","canonical_record":{"source":{"id":"1604.02119","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-07T19:12:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"009b09923a26a637a6b0e6752a53a874a64327d32879011d33afcbd7a60f6e78","abstract_canon_sha256":"f76eca353e2dfdac9596c16b783d76e51aadbf46e3663267d87411b0a3ec4fcd"},"schema_version":"1.0"},"canonical_sha256":"fc0631b0c211abffd9893ad2455176421e9e5ed45864f25038c47c3d4e6d283e","source":{"kind":"arxiv","id":"1604.02119","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02119","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02119v4","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02119","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"pith_short_12","alias_value":"7QDDDMGCCGV7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7QDDDMGCCGV77WMJ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7QDDDMGC","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7QDDDMGCCGV77WMJHLJEKULWII","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02119","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-07T19:12:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"009b09923a26a637a6b0e6752a53a874a64327d32879011d33afcbd7a60f6e78","abstract_canon_sha256":"f76eca353e2dfdac9596c16b783d76e51aadbf46e3663267d87411b0a3ec4fcd"},"schema_version":"1.0"},"canonical_sha256":"fc0631b0c211abffd9893ad2455176421e9e5ed45864f25038c47c3d4e6d283e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:02.819826Z","signature_b64":"muJtRsbN2+CjUanmdInjRkfRrMosbZCVgABbPKSV9Zl7WqKe69mG6Ik2iKVVqQOL9Q8SHNB7SZjA2Hkbv5qBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc0631b0c211abffd9893ad2455176421e9e5ed45864f25038c47c3d4e6d283e","last_reissued_at":"2026-05-18T00:28:02.819138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:02.819138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02119","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xo8fPSoKU4srB/JC6flYGhGvidEPxzzoWFw+rDKfTDUzWMHzOvwY8EvohoaLsDDz1LVcOX2hCm3y9xWfwZURDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:28:16.859693Z"},"content_sha256":"de4a61a9c445856fb97afb623f35f4bd519557ae42e64e7763214a80d45fa8c0","schema_version":"1.0","event_id":"sha256:de4a61a9c445856fb97afb623f35f4bd519557ae42e64e7763214a80d45fa8c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7QDDDMGCCGV77WMJHLJEKULWII","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Data processing for the sandwiched R\\'enyi divergence: a condition for equality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Cambyse Rouz\\'e, Felix Leditzky, Nilanjana Datta","submitted_at":"2016-04-07T19:12:05Z","abstract_excerpt":"The $\\alpha$-sandwiched R\\'enyi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\\alpha\\geq 1/2$. In this article, we derive a necessary and sufficient algebraic condition for equality in the data processing inequality for the $\\alpha$-sandwiched R\\'enyi divergence for all $\\alpha\\geq 1/2$. For the range $\\alpha\\in [1/2,1)$, our result provides the only condition for equality obtained thus far. To prove our result, we first consider the special case of partial trace, and derive a condition for equality based on the original proof of the data"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02119","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V42AZBou8FXXQPJ8NvwiL5oTf7lru/ZCryVHU75AxUBiz+KHRTXwhIN9j43QcGgyQUE/RnmGv3DwpIFhLRUnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:28:16.860393Z"},"content_sha256":"27d2cbabd3d8d17a67d319989f800e6c7f6e585e5208d870cc7ea2713a17433d","schema_version":"1.0","event_id":"sha256:27d2cbabd3d8d17a67d319989f800e6c7f6e585e5208d870cc7ea2713a17433d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QDDDMGCCGV77WMJHLJEKULWII/bundle.json","state_url":"https://pith.science/pith/7QDDDMGCCGV77WMJHLJEKULWII/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QDDDMGCCGV77WMJHLJEKULWII/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":"2026-05-31T00:28:16Z","links":{"resolver":"https://pith.science/pith/7QDDDMGCCGV77WMJHLJEKULWII","bundle":"https://pith.science/pith/7QDDDMGCCGV77WMJHLJEKULWII/bundle.json","state":"https://pith.science/pith/7QDDDMGCCGV77WMJHLJEKULWII/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QDDDMGCCGV77WMJHLJEKULWII/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7QDDDMGCCGV77WMJHLJEKULWII","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":"f76eca353e2dfdac9596c16b783d76e51aadbf46e3663267d87411b0a3ec4fcd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-07T19:12:05Z","title_canon_sha256":"009b09923a26a637a6b0e6752a53a874a64327d32879011d33afcbd7a60f6e78"},"schema_version":"1.0","source":{"id":"1604.02119","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02119","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02119v4","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02119","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"pith_short_12","alias_value":"7QDDDMGCCGV7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7QDDDMGCCGV77WMJ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7QDDDMGC","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:27d2cbabd3d8d17a67d319989f800e6c7f6e585e5208d870cc7ea2713a17433d","target":"graph","created_at":"2026-05-18T00:28:02Z","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 $\\alpha$-sandwiched R\\'enyi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\\alpha\\geq 1/2$. In this article, we derive a necessary and sufficient algebraic condition for equality in the data processing inequality for the $\\alpha$-sandwiched R\\'enyi divergence for all $\\alpha\\geq 1/2$. For the range $\\alpha\\in [1/2,1)$, our result provides the only condition for equality obtained thus far. To prove our result, we first consider the special case of partial trace, and derive a condition for equality based on the original proof of the data","authors_text":"Cambyse Rouz\\'e, Felix Leditzky, Nilanjana Datta","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-07T19:12:05Z","title":"Data processing for the sandwiched R\\'enyi divergence: a condition for equality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02119","kind":"arxiv","version":4},"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:de4a61a9c445856fb97afb623f35f4bd519557ae42e64e7763214a80d45fa8c0","target":"record","created_at":"2026-05-18T00:28:02Z","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":"f76eca353e2dfdac9596c16b783d76e51aadbf46e3663267d87411b0a3ec4fcd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-07T19:12:05Z","title_canon_sha256":"009b09923a26a637a6b0e6752a53a874a64327d32879011d33afcbd7a60f6e78"},"schema_version":"1.0","source":{"id":"1604.02119","kind":"arxiv","version":4}},"canonical_sha256":"fc0631b0c211abffd9893ad2455176421e9e5ed45864f25038c47c3d4e6d283e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc0631b0c211abffd9893ad2455176421e9e5ed45864f25038c47c3d4e6d283e","first_computed_at":"2026-05-18T00:28:02.819138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:02.819138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"muJtRsbN2+CjUanmdInjRkfRrMosbZCVgABbPKSV9Zl7WqKe69mG6Ik2iKVVqQOL9Q8SHNB7SZjA2Hkbv5qBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:02.819826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02119","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de4a61a9c445856fb97afb623f35f4bd519557ae42e64e7763214a80d45fa8c0","sha256:27d2cbabd3d8d17a67d319989f800e6c7f6e585e5208d870cc7ea2713a17433d"],"state_sha256":"51ae3d1885b50e7dd6d9bf9469f003833b6112b847adb868276275726920fad3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H3MC1cdektloCioyy16Ug2KnsmAhUZ3Y7opTMO3LKJUe0iylwB6MMXc5CpHNfjXMdJG30t3UVxRbuSJJWDRTBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:28:16.864173Z","bundle_sha256":"883c26b9e6658474282ea61a50200a52ca4b66674c2a865aba9a249fdbe26b06"}}