{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5ASO27RECCTZ5MZ3BJNHPIWF67","short_pith_number":"pith:5ASO27RE","canonical_record":{"source":{"id":"1510.06672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-10-22T16:12:03Z","cross_cats_sorted":["math-ph","math.MP","math.OA"],"title_canon_sha256":"544fa43879b3af676c91cd176e2511d6e16443b84a670fd2c9b49d3d6a245b43","abstract_canon_sha256":"6a9f2514dc1ba7f28a442b004e6cd20231efeec442c5832ebf6fc0e089a8a55b"},"schema_version":"1.0"},"canonical_sha256":"e824ed7e2410a79eb33b0a5a77a2c5f7e4d7de7032c03f95901d637bd8eff08e","source":{"kind":"arxiv","id":"1510.06672","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06672","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06672v1","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06672","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"5ASO27RECCTZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5ASO27RECCTZ5MZ3","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5ASO27RE","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5ASO27RECCTZ5MZ3BJNHPIWF67","target":"record","payload":{"canonical_record":{"source":{"id":"1510.06672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-10-22T16:12:03Z","cross_cats_sorted":["math-ph","math.MP","math.OA"],"title_canon_sha256":"544fa43879b3af676c91cd176e2511d6e16443b84a670fd2c9b49d3d6a245b43","abstract_canon_sha256":"6a9f2514dc1ba7f28a442b004e6cd20231efeec442c5832ebf6fc0e089a8a55b"},"schema_version":"1.0"},"canonical_sha256":"e824ed7e2410a79eb33b0a5a77a2c5f7e4d7de7032c03f95901d637bd8eff08e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:44.092959Z","signature_b64":"G+opfaobEl7DDuAs3+1b6xY4HHxagU0Uf37jAQT/5Y4uPjenz1l4g7vauc9jXCbqTKr4KaI0vYtoYqzQ5850Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e824ed7e2410a79eb33b0a5a77a2c5f7e4d7de7032c03f95901d637bd8eff08e","last_reissued_at":"2026-05-18T00:07:44.092417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:44.092417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.06672","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":"2026-05-18T00:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5kESP/6W3DgJwshHvMb0nz3Idm5YCfKJanvj8ML6g1AiA8qEnRYXAQOYFDBwMattmkSFe6kXbtMpmbBF/q+EDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:07:24.127305Z"},"content_sha256":"ca1b57c0a5dfc0c6daac2b75ed68d7045a99f813cb77b42ff75239ca029c0db4","schema_version":"1.0","event_id":"sha256:ca1b57c0a5dfc0c6daac2b75ed68d7045a99f813cb77b42ff75239ca029c0db4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5ASO27RECCTZ5MZ3BJNHPIWF67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Private algebras in quantum information and infinite-dimensional complementarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"David W. Kribs, Ivan G. Todorov, Jason Crann, Rupert H. Levene","submitted_at":"2015-10-22T16:12:03Z","abstract_excerpt":"We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06672","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":"2026-05-18T00:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7k8BJa4mSXH2Hj/BKKgEeblZFD4/vhLKQ99QoMxnuLWkfWZieHKds+TNewOMlpXvPNCIDRBQ9tE42Ws3NgZaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:07:24.127681Z"},"content_sha256":"54e01dc10ace0b2b11e44f847c7c7a4903e3622c42a37bc147464fed35adf961","schema_version":"1.0","event_id":"sha256:54e01dc10ace0b2b11e44f847c7c7a4903e3622c42a37bc147464fed35adf961"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ASO27RECCTZ5MZ3BJNHPIWF67/bundle.json","state_url":"https://pith.science/pith/5ASO27RECCTZ5MZ3BJNHPIWF67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ASO27RECCTZ5MZ3BJNHPIWF67/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":"2026-06-11T14:07:24Z","links":{"resolver":"https://pith.science/pith/5ASO27RECCTZ5MZ3BJNHPIWF67","bundle":"https://pith.science/pith/5ASO27RECCTZ5MZ3BJNHPIWF67/bundle.json","state":"https://pith.science/pith/5ASO27RECCTZ5MZ3BJNHPIWF67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ASO27RECCTZ5MZ3BJNHPIWF67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5ASO27RECCTZ5MZ3BJNHPIWF67","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":"6a9f2514dc1ba7f28a442b004e6cd20231efeec442c5832ebf6fc0e089a8a55b","cross_cats_sorted":["math-ph","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-10-22T16:12:03Z","title_canon_sha256":"544fa43879b3af676c91cd176e2511d6e16443b84a670fd2c9b49d3d6a245b43"},"schema_version":"1.0","source":{"id":"1510.06672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06672","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06672v1","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06672","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"5ASO27RECCTZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5ASO27RECCTZ5MZ3","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5ASO27RE","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:54e01dc10ace0b2b11e44f847c7c7a4903e3622c42a37bc147464fed35adf961","target":"graph","created_at":"2026-05-18T00:07:44Z","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 introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem.","authors_text":"David W. Kribs, Ivan G. Todorov, Jason Crann, Rupert H. Levene","cross_cats":["math-ph","math.MP","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-10-22T16:12:03Z","title":"Private algebras in quantum information and infinite-dimensional complementarity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06672","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:ca1b57c0a5dfc0c6daac2b75ed68d7045a99f813cb77b42ff75239ca029c0db4","target":"record","created_at":"2026-05-18T00:07:44Z","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":"6a9f2514dc1ba7f28a442b004e6cd20231efeec442c5832ebf6fc0e089a8a55b","cross_cats_sorted":["math-ph","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-10-22T16:12:03Z","title_canon_sha256":"544fa43879b3af676c91cd176e2511d6e16443b84a670fd2c9b49d3d6a245b43"},"schema_version":"1.0","source":{"id":"1510.06672","kind":"arxiv","version":1}},"canonical_sha256":"e824ed7e2410a79eb33b0a5a77a2c5f7e4d7de7032c03f95901d637bd8eff08e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e824ed7e2410a79eb33b0a5a77a2c5f7e4d7de7032c03f95901d637bd8eff08e","first_computed_at":"2026-05-18T00:07:44.092417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:44.092417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G+opfaobEl7DDuAs3+1b6xY4HHxagU0Uf37jAQT/5Y4uPjenz1l4g7vauc9jXCbqTKr4KaI0vYtoYqzQ5850Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:44.092959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca1b57c0a5dfc0c6daac2b75ed68d7045a99f813cb77b42ff75239ca029c0db4","sha256:54e01dc10ace0b2b11e44f847c7c7a4903e3622c42a37bc147464fed35adf961"],"state_sha256":"d191ac12a1a461f578747d40476bf8691b0f5bc0f0baccb78177613c9d4f8e88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0jjTNCeCr5K/RIBzi6g85Lqpn48z7b3BYXGvmXbH2+FtzbeQOOCpb0uFtABEELDqMpt3+V0TfoofB0/F+FRUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:07:24.130098Z","bundle_sha256":"b8a606d32d3dd4618b8f36ee68af4a38ab7d8f5cf43316397bdd197547f7bebc"}}