{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QATP5OLOIZVNUYICFDT46756GL","short_pith_number":"pith:QATP5OLO","canonical_record":{"source":{"id":"1511.07099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-23T02:46:50Z","cross_cats_sorted":[],"title_canon_sha256":"38dae789b290a0cbb672bd3052436ecdedfbce2d3861273c8595e0b4f331894c","abstract_canon_sha256":"a583748cdf005f3816cd9ae952263056a6bb2571dd6746067a5bd9d5819f7e3b"},"schema_version":"1.0"},"canonical_sha256":"8026feb96e466ada610228e7cf7fbe32c9fd6e01033d56ba2d4b73085fa2d0e5","source":{"kind":"arxiv","id":"1511.07099","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07099","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07099v2","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07099","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"QATP5OLOIZVN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QATP5OLOIZVNUYIC","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QATP5OLO","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QATP5OLOIZVNUYICFDT46756GL","target":"record","payload":{"canonical_record":{"source":{"id":"1511.07099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-23T02:46:50Z","cross_cats_sorted":[],"title_canon_sha256":"38dae789b290a0cbb672bd3052436ecdedfbce2d3861273c8595e0b4f331894c","abstract_canon_sha256":"a583748cdf005f3816cd9ae952263056a6bb2571dd6746067a5bd9d5819f7e3b"},"schema_version":"1.0"},"canonical_sha256":"8026feb96e466ada610228e7cf7fbe32c9fd6e01033d56ba2d4b73085fa2d0e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:14.860585Z","signature_b64":"PCjuefI0l5RJxa1yTOdA28VINa+q+fvfCGSZ6K+wcHwjeL7hpuhN75MRiTJRMD+Hrh0IrLjKARf/Ipy4l459BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8026feb96e466ada610228e7cf7fbe32c9fd6e01033d56ba2d4b73085fa2d0e5","last_reissued_at":"2026-05-18T01:10:14.860166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:14.860166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.07099","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3Q2yPB9dUY6nYa8j7ens5CMfIqV77h7q1lfsM5fWk4FCHvznvg6aWqhqKCqAwvZeSrn9x9qvgYq5NBLrAp/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:26:33.068524Z"},"content_sha256":"f1423b028b1f9299f4fc7c578d83f502e8040894115680c4967597d6c567ffd1","schema_version":"1.0","event_id":"sha256:f1423b028b1f9299f4fc7c578d83f502e8040894115680c4967597d6c567ffd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QATP5OLOIZVNUYICFDT46756GL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Majorization entropic uncertainty relations for quantum operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexey E. Rastegin, Karol \\.Zyczkowski","submitted_at":"2015-11-23T02:46:50Z","abstract_excerpt":"Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an extension of the previous formulation, which deals with submatrices of a unitary matrix relating orthogonal bases in which measurements are performed. Two classes of majorization relations are considered: one related to tensor product of probability vectors and another one related to their direct sum. We explicitly discuss an example of a pair of one-qubit oper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07099","kind":"arxiv","version":2},"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":"2026-05-18T01:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVHuZ1l4TpGnAyakbp3QmBU4giGygd75VAgrPkynCmOTWHIZEVJinseZ9OVYS9hG5LK93envEQMVq1cdzZ/IDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:26:33.069174Z"},"content_sha256":"b99d71778ed4eb9501510ee5f9f545a769c4f28dd2d441825190fc13a83f7c8f","schema_version":"1.0","event_id":"sha256:b99d71778ed4eb9501510ee5f9f545a769c4f28dd2d441825190fc13a83f7c8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QATP5OLOIZVNUYICFDT46756GL/bundle.json","state_url":"https://pith.science/pith/QATP5OLOIZVNUYICFDT46756GL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QATP5OLOIZVNUYICFDT46756GL/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":"2026-05-30T02:26:33Z","links":{"resolver":"https://pith.science/pith/QATP5OLOIZVNUYICFDT46756GL","bundle":"https://pith.science/pith/QATP5OLOIZVNUYICFDT46756GL/bundle.json","state":"https://pith.science/pith/QATP5OLOIZVNUYICFDT46756GL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QATP5OLOIZVNUYICFDT46756GL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QATP5OLOIZVNUYICFDT46756GL","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":"a583748cdf005f3816cd9ae952263056a6bb2571dd6746067a5bd9d5819f7e3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-23T02:46:50Z","title_canon_sha256":"38dae789b290a0cbb672bd3052436ecdedfbce2d3861273c8595e0b4f331894c"},"schema_version":"1.0","source":{"id":"1511.07099","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07099","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07099v2","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07099","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"QATP5OLOIZVN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QATP5OLOIZVNUYIC","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QATP5OLO","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:b99d71778ed4eb9501510ee5f9f545a769c4f28dd2d441825190fc13a83f7c8f","target":"graph","created_at":"2026-05-18T01:10:14Z","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":"Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an extension of the previous formulation, which deals with submatrices of a unitary matrix relating orthogonal bases in which measurements are performed. Two classes of majorization relations are considered: one related to tensor product of probability vectors and another one related to their direct sum. We explicitly discuss an example of a pair of one-qubit oper","authors_text":"Alexey E. Rastegin, Karol \\.Zyczkowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-23T02:46:50Z","title":"Majorization entropic uncertainty relations for quantum operations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07099","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:f1423b028b1f9299f4fc7c578d83f502e8040894115680c4967597d6c567ffd1","target":"record","created_at":"2026-05-18T01:10:14Z","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":"a583748cdf005f3816cd9ae952263056a6bb2571dd6746067a5bd9d5819f7e3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-23T02:46:50Z","title_canon_sha256":"38dae789b290a0cbb672bd3052436ecdedfbce2d3861273c8595e0b4f331894c"},"schema_version":"1.0","source":{"id":"1511.07099","kind":"arxiv","version":2}},"canonical_sha256":"8026feb96e466ada610228e7cf7fbe32c9fd6e01033d56ba2d4b73085fa2d0e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8026feb96e466ada610228e7cf7fbe32c9fd6e01033d56ba2d4b73085fa2d0e5","first_computed_at":"2026-05-18T01:10:14.860166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:14.860166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PCjuefI0l5RJxa1yTOdA28VINa+q+fvfCGSZ6K+wcHwjeL7hpuhN75MRiTJRMD+Hrh0IrLjKARf/Ipy4l459BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:14.860585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1423b028b1f9299f4fc7c578d83f502e8040894115680c4967597d6c567ffd1","sha256:b99d71778ed4eb9501510ee5f9f545a769c4f28dd2d441825190fc13a83f7c8f"],"state_sha256":"306bec552a49732d75c87755157878fb762afd0c2d5b1579c4445978f0db0738"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G5rS0GtDJUxYr7GKWaKkZ1ZGmM+2fhIPZY2ZGKJKkqS4R1QVVEkXLMH05Z9/x4aSjCJlBeUAPYsay9qQzviHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:26:33.072409Z","bundle_sha256":"5b4368f44c1059b7c85f040f2c72a87e72feda764a0053893917719781ff9651"}}