{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QU7Q3TBMMFEC7BDN62KWKF6SNW","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":"a01ef110bc5c437e06351b9b4ab98050d129d6b80b4830d3c04385f75cfe96bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-03-07T11:59:35Z","title_canon_sha256":"bf102eeffddb0030ca5e1e386ee97e4ca24aaff88455aa6a167c04d69b6f3215"},"schema_version":"1.0","source":{"id":"0903.1340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1340","created_at":"2026-05-18T03:24:42Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1340v1","created_at":"2026-05-18T03:24:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1340","created_at":"2026-05-18T03:24:42Z"},{"alias_kind":"pith_short_12","alias_value":"QU7Q3TBMMFEC","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QU7Q3TBMMFEC7BDN","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QU7Q3TBM","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:c08b564a6002f8045440eea85b72fa923aad236e231bb9c8204829756832d8df","target":"graph","created_at":"2026-05-18T03:24:42Z","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":"Explicit expressions for the concurrence of all positive and trace-preserving (\"stochastic\") 1-qubit maps are presented. We construct the relevant convex roof patterns by a new method. We conclude that two component optimal decompositions always exist. Our results can be transferred to 2xN-quantumsystems providing the concurrence for all rank two density operators as well as lower and upper bounds for their entanglement of formation.\n  We apply these results to a study of the entanglement entropy of 1-qubit stochastic maps which preserve axial symmetry. Using analytic and numeric results we an","authors_text":"Armin Uhlmann, Meik Hellmund","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-03-07T11:59:35Z","title":"Concurrence and Entanglement Entropy of Stochastic 1-Qubit Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1340","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:b19e2c1f788bce2ee54b3399d420afe506715f3baa17f49eb36211b80f4358fa","target":"record","created_at":"2026-05-18T03:24:42Z","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":"a01ef110bc5c437e06351b9b4ab98050d129d6b80b4830d3c04385f75cfe96bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-03-07T11:59:35Z","title_canon_sha256":"bf102eeffddb0030ca5e1e386ee97e4ca24aaff88455aa6a167c04d69b6f3215"},"schema_version":"1.0","source":{"id":"0903.1340","kind":"arxiv","version":1}},"canonical_sha256":"853f0dcc2c61482f846df6956517d26d9a5cc4d9a74097d8811f4fd229ebc910","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"853f0dcc2c61482f846df6956517d26d9a5cc4d9a74097d8811f4fd229ebc910","first_computed_at":"2026-05-18T03:24:42.337416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:42.337416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oE3AoTk2vkB9og6kzTy1NveBkHvLmG+VVw7JJksmdaFq3SDvJKsuDAbana9UWfZOWqc/0nXDeUTFIkfiemcmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:42.338087Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.1340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b19e2c1f788bce2ee54b3399d420afe506715f3baa17f49eb36211b80f4358fa","sha256:c08b564a6002f8045440eea85b72fa923aad236e231bb9c8204829756832d8df"],"state_sha256":"017d949b55831a219f493baf967a80131c9a719d978470992fa856c2bd19ea06"}