{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BY36LH2KLZWTRFFQFKWJKEU4E5","short_pith_number":"pith:BY36LH2K","schema_version":"1.0","canonical_sha256":"0e37e59f4a5e6d3894b02aac95129c274582166bb4f174f956dd0c6d79529eae","source":{"kind":"arxiv","id":"1610.00930","version":1},"attestation_state":"computed","paper":{"title":"Nuclear Numerical Range and Quantum Error Correction Codes for non-unitary noise models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Karol \\.Zyczkowski, Patryk Lipka-Bartosik","submitted_at":"2016-10-04T11:07:15Z","abstract_excerpt":"We introduce a notion of nuclear numerical range defined as the set of expectation values of a given operator $A$ among normalized pure states, which belong to the nucleus of an auxiliary operator $Z$. This notion proves to be applicable to investigate models of quantum noise with block-diagonal structure of the corresponding Kraus operators. The problem of constructing a suitable quantum error correction code for this model can be restated as a geometric problem of finding intersection points of certain sets in the complex plane. This technique, worked out in the case of two-qubit systems, ca"},"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":"1610.00930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-04T11:07:15Z","cross_cats_sorted":[],"title_canon_sha256":"3c8f7d9432693cb6acaa97d6514b45c5d1aa7595b9f2177264b51ea9c955e526","abstract_canon_sha256":"4f81d81bc9ad168e66915713b642e1ccc3dce54a65ecf1cacb132bac91faa70b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:57.543483Z","signature_b64":"msCx/veUSikYpO5HRryolOZnvaOSUccnFDB4MHr5kbLDUWoTpAe3hqQqzXMVmrymKQIrxu1d/gXx1eE9ZiN5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e37e59f4a5e6d3894b02aac95129c274582166bb4f174f956dd0c6d79529eae","last_reissued_at":"2026-05-18T00:51:57.542820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:57.542820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nuclear Numerical Range and Quantum Error Correction Codes for non-unitary noise models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Karol \\.Zyczkowski, Patryk Lipka-Bartosik","submitted_at":"2016-10-04T11:07:15Z","abstract_excerpt":"We introduce a notion of nuclear numerical range defined as the set of expectation values of a given operator $A$ among normalized pure states, which belong to the nucleus of an auxiliary operator $Z$. This notion proves to be applicable to investigate models of quantum noise with block-diagonal structure of the corresponding Kraus operators. The problem of constructing a suitable quantum error correction code for this model can be restated as a geometric problem of finding intersection points of certain sets in the complex plane. This technique, worked out in the case of two-qubit systems, ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00930","kind":"arxiv","version":1},"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":"1610.00930","created_at":"2026-05-18T00:51:57.542931+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.00930v1","created_at":"2026-05-18T00:51:57.542931+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00930","created_at":"2026-05-18T00:51:57.542931+00:00"},{"alias_kind":"pith_short_12","alias_value":"BY36LH2KLZWT","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BY36LH2KLZWTRFFQ","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BY36LH2K","created_at":"2026-05-18T12:30:09.641336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BY36LH2KLZWTRFFQFKWJKEU4E5","json":"https://pith.science/pith/BY36LH2KLZWTRFFQFKWJKEU4E5.json","graph_json":"https://pith.science/api/pith-number/BY36LH2KLZWTRFFQFKWJKEU4E5/graph.json","events_json":"https://pith.science/api/pith-number/BY36LH2KLZWTRFFQFKWJKEU4E5/events.json","paper":"https://pith.science/paper/BY36LH2K"},"agent_actions":{"view_html":"https://pith.science/pith/BY36LH2KLZWTRFFQFKWJKEU4E5","download_json":"https://pith.science/pith/BY36LH2KLZWTRFFQFKWJKEU4E5.json","view_paper":"https://pith.science/paper/BY36LH2K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.00930&json=true","fetch_graph":"https://pith.science/api/pith-number/BY36LH2KLZWTRFFQFKWJKEU4E5/graph.json","fetch_events":"https://pith.science/api/pith-number/BY36LH2KLZWTRFFQFKWJKEU4E5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BY36LH2KLZWTRFFQFKWJKEU4E5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BY36LH2KLZWTRFFQFKWJKEU4E5/action/storage_attestation","attest_author":"https://pith.science/pith/BY36LH2KLZWTRFFQFKWJKEU4E5/action/author_attestation","sign_citation":"https://pith.science/pith/BY36LH2KLZWTRFFQFKWJKEU4E5/action/citation_signature","submit_replication":"https://pith.science/pith/BY36LH2KLZWTRFFQFKWJKEU4E5/action/replication_record"}},"created_at":"2026-05-18T00:51:57.542931+00:00","updated_at":"2026-05-18T00:51:57.542931+00:00"}