{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CWYWNTFZPKCWUDQ5VJFAJMWLXM","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":"80dbe8001f0ad15af2349543a7dbac655ccf37e0d844f155da0bac6f015e11fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-06T20:00:28Z","title_canon_sha256":"434e7516a756e45f17cae39c150dcb7eb329f9047f48ecf2dd3ba5db1d5328c3"},"schema_version":"1.0","source":{"id":"1004.0951","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0951","created_at":"2026-05-18T04:29:35Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0951v2","created_at":"2026-05-18T04:29:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0951","created_at":"2026-05-18T04:29:35Z"},{"alias_kind":"pith_short_12","alias_value":"CWYWNTFZPKCW","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CWYWNTFZPKCWUDQ5","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CWYWNTFZ","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:5d6c7aa2e48ed91c328e05ddcd93e566763956b4c4015e426fdb106b1e799e5f","target":"graph","created_at":"2026-05-18T04:29:35Z","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":"A dynamical map is a map which takes one density operator to another. Such a map can be written in an operator-sum representation (OSR) using a spectral decomposition.  The method of the construction applies to more general maps which need not be completely positive.  The OSR not unique; there is a freedom to choose the set of operators in the OSR differently, yet still obtain the same map.  Here we identify all maps which are equivalent to a given map.  Whereas the freedom for completely positive maps is unitary, the freedom for maps which are not necessarily completely positive is pseudo-uni","authors_text":"Mark S. Byrd, Yong-Cheng Ou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-06T20:00:28Z","title":"All maps equivalent to a given map, completely positive or not"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0951","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:feb136a675ff1071c8636058a30f51298cf9042a7e176bbb46e318e8f52a11cc","target":"record","created_at":"2026-05-18T04:29:35Z","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":"80dbe8001f0ad15af2349543a7dbac655ccf37e0d844f155da0bac6f015e11fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-06T20:00:28Z","title_canon_sha256":"434e7516a756e45f17cae39c150dcb7eb329f9047f48ecf2dd3ba5db1d5328c3"},"schema_version":"1.0","source":{"id":"1004.0951","kind":"arxiv","version":2}},"canonical_sha256":"15b166ccb97a856a0e1daa4a04b2cbbb2faac14a7a1532175aa13bb1c7951e9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15b166ccb97a856a0e1daa4a04b2cbbb2faac14a7a1532175aa13bb1c7951e9c","first_computed_at":"2026-05-18T04:29:35.005259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:35.005259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LASV+G7NgsUY4am/nmy9iGVDbDoF8NgTQjooms7GnM74Qx3d9XkjIuUMxdvjVTx9A63A4ADQz1wIpP4OCkvLCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:35.005644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0951","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:feb136a675ff1071c8636058a30f51298cf9042a7e176bbb46e318e8f52a11cc","sha256:5d6c7aa2e48ed91c328e05ddcd93e566763956b4c4015e426fdb106b1e799e5f"],"state_sha256":"74aa1afb93f61ef467325e4609c1bf267cbadfbbfc69f51dcbe1153e5dcebc1a"}