{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:LMRULMN6IWK26DXG4XJNEPYNDJ","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":"3234f3cc58f2ad6d2e6a79bd1af5c7ee636d72f0a8cd52889b51cea3322ffeef","cross_cats_sorted":["math-ph","math.MP","math.OA","math.RA"],"license":"","primary_cat":"quant-ph","submitted_at":"2000-12-31T22:34:10Z","title_canon_sha256":"b634f34f8f176f1b65a58b81ee5936287f6b6d58d7b7d4d396ff3264e8a15e0c"},"schema_version":"1.0","source":{"id":"quant-ph/0101003","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0101003","created_at":"2026-07-04T15:51:37Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0101003v2","created_at":"2026-07-04T15:51:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0101003","created_at":"2026-07-04T15:51:37Z"},{"alias_kind":"pith_short_12","alias_value":"LMRULMN6IWK2","created_at":"2026-07-04T15:51:37Z"},{"alias_kind":"pith_short_16","alias_value":"LMRULMN6IWK26DXG","created_at":"2026-07-04T15:51:37Z"},{"alias_kind":"pith_short_8","alias_value":"LMRULMN6","created_at":"2026-07-04T15:51:37Z"}],"graph_snapshots":[{"event_id":"sha256:33514102445db9a7dc76d2cd654db7f68d8bdc2c4ce9cb2db9db990a704ef768","target":"graph","created_at":"2026-07-04T15:51:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0101003/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any trace-preserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduction to a certain canonical form. This allows a detailed examination of an important class of non-unital extreme points which can be characterized as having exactly two images on the Bloch sphere.\n  We also discuss a number of related issues about","authors_text":"Elisabeth Werner, Mary Beth Ruskai, Stanislaw Szarek","cross_cats":["math-ph","math.MP","math.OA","math.RA"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2000-12-31T22:34:10Z","title":"An Analysis of Completely-Positive Trace-Preserving Maps on 2x2 Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0101003","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":"sha256:10fabd3a90af13c5134174c80197cee6603d7173aa96327d840945f763ba2bd1","target":"record","created_at":"2026-07-04T15:51:37Z","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":"3234f3cc58f2ad6d2e6a79bd1af5c7ee636d72f0a8cd52889b51cea3322ffeef","cross_cats_sorted":["math-ph","math.MP","math.OA","math.RA"],"license":"","primary_cat":"quant-ph","submitted_at":"2000-12-31T22:34:10Z","title_canon_sha256":"b634f34f8f176f1b65a58b81ee5936287f6b6d58d7b7d4d396ff3264e8a15e0c"},"schema_version":"1.0","source":{"id":"quant-ph/0101003","kind":"arxiv","version":2}},"canonical_sha256":"5b2345b1be4595af0ee6e5d2d23f0d1a4f91a1bb60c058c1114d00d2e7ab0d43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b2345b1be4595af0ee6e5d2d23f0d1a4f91a1bb60c058c1114d00d2e7ab0d43","first_computed_at":"2026-07-04T15:51:37.398602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:51:37.398602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d1ekUCkqjDP0c/UiAkpia0DwI5GIi4OZJyDQszsz1GiCTYqWk0SJ414Q6XNnUNt/tTg7ZQ7fEfnOgo6HxBtjCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:51:37.399019Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0101003","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10fabd3a90af13c5134174c80197cee6603d7173aa96327d840945f763ba2bd1","sha256:33514102445db9a7dc76d2cd654db7f68d8bdc2c4ce9cb2db9db990a704ef768"],"state_sha256":"e066106605ea99d5b44412f6b9438857bb8b5cb41899adc56c580006844b48f6"}