{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AMRWFCYG2MILG5Z5HNNGVATEVP","short_pith_number":"pith:AMRWFCYG","canonical_record":{"source":{"id":"1709.01752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-06T09:59:21Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"b436e1b4f6a260db93d96c3870bd6ae1fb09efc26a3c03a42747a6af8c058dd0","abstract_canon_sha256":"6ab3169c2913ba228665481f7150dd9a3a27d100793808e1f14834bf1b67a2e2"},"schema_version":"1.0"},"canonical_sha256":"0323628b06d310b3773d3b5a6a8264abfb851ba86590a0258b9ba1bfaff24449","source":{"kind":"arxiv","id":"1709.01752","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01752","created_at":"2026-05-18T00:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01752v1","created_at":"2026-05-18T00:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01752","created_at":"2026-05-18T00:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"AMRWFCYG2MIL","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AMRWFCYG2MILG5Z5","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AMRWFCYG","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AMRWFCYG2MILG5Z5HNNGVATEVP","target":"record","payload":{"canonical_record":{"source":{"id":"1709.01752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-06T09:59:21Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"b436e1b4f6a260db93d96c3870bd6ae1fb09efc26a3c03a42747a6af8c058dd0","abstract_canon_sha256":"6ab3169c2913ba228665481f7150dd9a3a27d100793808e1f14834bf1b67a2e2"},"schema_version":"1.0"},"canonical_sha256":"0323628b06d310b3773d3b5a6a8264abfb851ba86590a0258b9ba1bfaff24449","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:33.753370Z","signature_b64":"1ivftMwbzr4iOEoYSUxRG+tkmtcmOAFLsMeGfFQseR01ShsS2RMGLRKtrDJkJpIDsbD4zoF1VBsXBGQm2Vl6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0323628b06d310b3773d3b5a6a8264abfb851ba86590a0258b9ba1bfaff24449","last_reissued_at":"2026-05-18T00:23:33.752818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:33.752818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.01752","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cxbxPCUBEJhLoTe7PbgSqQnz4NjcuL65fw80HwiX5WHPxv1g8GsbZvWekKQsUUnB0b35TJcuqCdNdrz6RoaIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:59:40.214689Z"},"content_sha256":"88a7d473e47b0e811c8e97d7cac210d9436b5d36219af2eb82209efb778fbfc6","schema_version":"1.0","event_id":"sha256:88a7d473e47b0e811c8e97d7cac210d9436b5d36219af2eb82209efb778fbfc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AMRWFCYG2MILG5Z5HNNGVATEVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Privacy and Schur Product Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"David W. Kribs, Jeremy Levick, Rajesh Pereira","submitted_at":"2017-09-06T09:59:21Z","abstract_excerpt":"We investigate the quantum privacy properties of an important class of quantum chan-nels, by making use of a connection with Schur product matrix operations and associated correlationmatrix structures. For channels implemented by mutually commuting unitaries, which cannot priva-tise qubits encoded directly into subspaces, we nevertheless identify private algebras and subsystemsthat can be privatised by the channels. We also obtain further results by combining our analysiswith tools from the theory of quasiorthogonal operator algebras and graph theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01752","kind":"arxiv","version":1},"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":"2026-05-18T00:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ogGSt8By6K6Kc05S3Ddw/9F0+FgOJ7UOmzE/je7V3cUqKBwiMbbiOrUvUTc3CZIR0uRTPNo7hRgMtaoLF1XPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:59:40.215033Z"},"content_sha256":"cbe017275d588d3d49ed900fd6aa5f2c1df948890dd483bf0ea593242096797d","schema_version":"1.0","event_id":"sha256:cbe017275d588d3d49ed900fd6aa5f2c1df948890dd483bf0ea593242096797d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMRWFCYG2MILG5Z5HNNGVATEVP/bundle.json","state_url":"https://pith.science/pith/AMRWFCYG2MILG5Z5HNNGVATEVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMRWFCYG2MILG5Z5HNNGVATEVP/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":"2026-06-08T09:59:40Z","links":{"resolver":"https://pith.science/pith/AMRWFCYG2MILG5Z5HNNGVATEVP","bundle":"https://pith.science/pith/AMRWFCYG2MILG5Z5HNNGVATEVP/bundle.json","state":"https://pith.science/pith/AMRWFCYG2MILG5Z5HNNGVATEVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMRWFCYG2MILG5Z5HNNGVATEVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AMRWFCYG2MILG5Z5HNNGVATEVP","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":"6ab3169c2913ba228665481f7150dd9a3a27d100793808e1f14834bf1b67a2e2","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-06T09:59:21Z","title_canon_sha256":"b436e1b4f6a260db93d96c3870bd6ae1fb09efc26a3c03a42747a6af8c058dd0"},"schema_version":"1.0","source":{"id":"1709.01752","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01752","created_at":"2026-05-18T00:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01752v1","created_at":"2026-05-18T00:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01752","created_at":"2026-05-18T00:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"AMRWFCYG2MIL","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AMRWFCYG2MILG5Z5","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AMRWFCYG","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:cbe017275d588d3d49ed900fd6aa5f2c1df948890dd483bf0ea593242096797d","target":"graph","created_at":"2026-05-18T00:23:33Z","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":"We investigate the quantum privacy properties of an important class of quantum chan-nels, by making use of a connection with Schur product matrix operations and associated correlationmatrix structures. For channels implemented by mutually commuting unitaries, which cannot priva-tise qubits encoded directly into subspaces, we nevertheless identify private algebras and subsystemsthat can be privatised by the channels. We also obtain further results by combining our analysiswith tools from the theory of quasiorthogonal operator algebras and graph theory.","authors_text":"David W. Kribs, Jeremy Levick, Rajesh Pereira","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-06T09:59:21Z","title":"Quantum Privacy and Schur Product Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01752","kind":"arxiv","version":1},"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":"sha256:88a7d473e47b0e811c8e97d7cac210d9436b5d36219af2eb82209efb778fbfc6","target":"record","created_at":"2026-05-18T00:23:33Z","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":"6ab3169c2913ba228665481f7150dd9a3a27d100793808e1f14834bf1b67a2e2","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-06T09:59:21Z","title_canon_sha256":"b436e1b4f6a260db93d96c3870bd6ae1fb09efc26a3c03a42747a6af8c058dd0"},"schema_version":"1.0","source":{"id":"1709.01752","kind":"arxiv","version":1}},"canonical_sha256":"0323628b06d310b3773d3b5a6a8264abfb851ba86590a0258b9ba1bfaff24449","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0323628b06d310b3773d3b5a6a8264abfb851ba86590a0258b9ba1bfaff24449","first_computed_at":"2026-05-18T00:23:33.752818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:33.752818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ivftMwbzr4iOEoYSUxRG+tkmtcmOAFLsMeGfFQseR01ShsS2RMGLRKtrDJkJpIDsbD4zoF1VBsXBGQm2Vl6Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:33.753370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01752","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88a7d473e47b0e811c8e97d7cac210d9436b5d36219af2eb82209efb778fbfc6","sha256:cbe017275d588d3d49ed900fd6aa5f2c1df948890dd483bf0ea593242096797d"],"state_sha256":"fac9ec8d249b3ac6a51dbce267dea94c81a141b136e4074b1fdbe34b5b4b600f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iz/wzCVBGAIcneDsvZazy+ZmpJ6EieG+/HmnHdG5ybBRxcqQeu41l4BBzTlmzZG4W92hygs60SvhQ36zMjAsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:59:40.217108Z","bundle_sha256":"97aa771a79e9abd92a1defcae7c33d93b66a4f4e9cf05169bdc02322c6c846ff"}}