{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:JYAYM3PVDZR5XXGDCYVJWPHRYY","short_pith_number":"pith:JYAYM3PV","schema_version":"1.0","canonical_sha256":"4e01866df51e63dbdcc3162a9b3cf1c616da14b5c6652016e5b5b7762d09612b","source":{"kind":"arxiv","id":"1012.3197","version":3},"attestation_state":"computed","paper":{"title":"Normal completely positive maps on the space of quantum operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. Toigo, G. Chiribella, V. Umanit\\`a","submitted_at":"2010-12-15T00:20:08Z","abstract_excerpt":"Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps transforming quantum operations with input in a separable von Neumann algebra and output in the algebra of the bounded operators on a given separable Hilbert space. In this setting we prove two dilation theorems for quantum supermaps that are the analogues of the Stinespring and Radon-Nikodym theorems for quantum operations. Finally, we consider the case of quant"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.3197","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-15T00:20:08Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"ef22604a15adf485f5d16a2ab927e0e95f4245c801561f093127e5573fc788e4","abstract_canon_sha256":"454f3038c336e4c02ec87cbc93a24b7d404a53b4ea9cd2a783d1579846056aac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:07.215722Z","signature_b64":"GdTw8hze2lSFb6BjKB/ldVvWCG7UuFDi6QYdHqxqGjJF3byrh4s0WFs3fQiX9guhsXMroc2nP3mg4b0sOHBCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e01866df51e63dbdcc3162a9b3cf1c616da14b5c6652016e5b5b7762d09612b","last_reissued_at":"2026-05-18T02:23:07.215125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:07.215125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normal completely positive maps on the space of quantum operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. Toigo, G. Chiribella, V. Umanit\\`a","submitted_at":"2010-12-15T00:20:08Z","abstract_excerpt":"Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps transforming quantum operations with input in a separable von Neumann algebra and output in the algebra of the bounded operators on a given separable Hilbert space. In this setting we prove two dilation theorems for quantum supermaps that are the analogues of the Stinespring and Radon-Nikodym theorems for quantum operations. Finally, we consider the case of quant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3197","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.3197","created_at":"2026-05-18T02:23:07.215210+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.3197v3","created_at":"2026-05-18T02:23:07.215210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3197","created_at":"2026-05-18T02:23:07.215210+00:00"},{"alias_kind":"pith_short_12","alias_value":"JYAYM3PVDZR5","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"JYAYM3PVDZR5XXGD","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"JYAYM3PV","created_at":"2026-05-18T12:26:09.077623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2207.09180","citing_title":"Polycategorical Constructions for Unitary Supermaps of Arbitrary Dimension","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JYAYM3PVDZR5XXGDCYVJWPHRYY","json":"https://pith.science/pith/JYAYM3PVDZR5XXGDCYVJWPHRYY.json","graph_json":"https://pith.science/api/pith-number/JYAYM3PVDZR5XXGDCYVJWPHRYY/graph.json","events_json":"https://pith.science/api/pith-number/JYAYM3PVDZR5XXGDCYVJWPHRYY/events.json","paper":"https://pith.science/paper/JYAYM3PV"},"agent_actions":{"view_html":"https://pith.science/pith/JYAYM3PVDZR5XXGDCYVJWPHRYY","download_json":"https://pith.science/pith/JYAYM3PVDZR5XXGDCYVJWPHRYY.json","view_paper":"https://pith.science/paper/JYAYM3PV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.3197&json=true","fetch_graph":"https://pith.science/api/pith-number/JYAYM3PVDZR5XXGDCYVJWPHRYY/graph.json","fetch_events":"https://pith.science/api/pith-number/JYAYM3PVDZR5XXGDCYVJWPHRYY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JYAYM3PVDZR5XXGDCYVJWPHRYY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JYAYM3PVDZR5XXGDCYVJWPHRYY/action/storage_attestation","attest_author":"https://pith.science/pith/JYAYM3PVDZR5XXGDCYVJWPHRYY/action/author_attestation","sign_citation":"https://pith.science/pith/JYAYM3PVDZR5XXGDCYVJWPHRYY/action/citation_signature","submit_replication":"https://pith.science/pith/JYAYM3PVDZR5XXGDCYVJWPHRYY/action/replication_record"}},"created_at":"2026-05-18T02:23:07.215210+00:00","updated_at":"2026-05-18T02:23:07.215210+00:00"}