{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TO6CHCUNT4O7JSC4BELSDK3UGR","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":"0a380eef87e0d49a72c7aeefd59682bd0f26ca81c3555e3c534c7f06f8efd268","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-08-10T18:38:54Z","title_canon_sha256":"e3c254e44775f171933786bdd6174b1feeb5dd920da40e2526184cf31c58f23e"},"schema_version":"1.0","source":{"id":"1208.2246","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2246","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2246v2","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2246","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"TO6CHCUNT4O7","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TO6CHCUNT4O7JSC4","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TO6CHCUN","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:c0de7ead72354aa5ee3f58eb294b55aae1b24c275a9ccb7d6fbe14f707e8c1a5","target":"graph","created_at":"2026-05-18T03:16:38Z","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 most general notion of a private quantum code, which involves the encoding of qubits into quantum subsystems and subspaces. We contribute to the structure theory for private quantum codes by deriving testable conditions for private quantum subsystems in terms of Kraus operators for channels; establishing an analogue of the Knill-Laflamme conditions in this setting. For a large class of naturally arising quantum channels, we show that private subsystems can exist even in the absence of private subspaces. In doing so, we also discover the first examples of private subsystems t","authors_text":"David W. Kribs, Raymond Laflamme, Sarah Plosker, Tomas Jochym-O'Connor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-08-10T18:38:54Z","title":"Private Quantum Subsystems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2246","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":"sha256:9e7aada631402f9e89f0e39a9237d76652f59f1a3e422deaab204bfa74a2b4d1","target":"record","created_at":"2026-05-18T03:16:38Z","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":"0a380eef87e0d49a72c7aeefd59682bd0f26ca81c3555e3c534c7f06f8efd268","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-08-10T18:38:54Z","title_canon_sha256":"e3c254e44775f171933786bdd6174b1feeb5dd920da40e2526184cf31c58f23e"},"schema_version":"1.0","source":{"id":"1208.2246","kind":"arxiv","version":2}},"canonical_sha256":"9bbc238a8d9f1df4c85c091721ab7434636622e5357b08e641b2e70dd3e721ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bbc238a8d9f1df4c85c091721ab7434636622e5357b08e641b2e70dd3e721ea","first_computed_at":"2026-05-18T03:16:38.631751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:38.631751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cVcO00DF+hLJq7nHmTEpwMX8kPcsAGiB3KsMRlAqJ6dLBr5GC3NMsgPVhU3uwYoYmYN55+Lg7q6gNBgfQciMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:38.632241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2246","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e7aada631402f9e89f0e39a9237d76652f59f1a3e422deaab204bfa74a2b4d1","sha256:c0de7ead72354aa5ee3f58eb294b55aae1b24c275a9ccb7d6fbe14f707e8c1a5"],"state_sha256":"b74b463c12574cac1571afa2e5d7b5e18e59130d2712dc2972c9b21d8c0dbed3"}