{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4DUDRAMABTCDL2HDBSS747VCX4","short_pith_number":"pith:4DUDRAMA","schema_version":"1.0","canonical_sha256":"e0e83881800cc435e8e30ca5fe7ea2bf2f98bba0d43e697fb2b050f19c1b9497","source":{"kind":"arxiv","id":"1908.08942","version":3},"attestation_state":"computed","paper":{"title":"Lyapunov exponents for Quantum Channels: an entropy formula and generic properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","quant-ph"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Jader E. Brasil, Josue Knorst","submitted_at":"2019-08-22T23:14:50Z","abstract_excerpt":"We denote by $M_k$ the set of $k$ by $k$ matrices with complex entries. We consider quantum channels $\\phi_L$ of the form: given a measurable function $L:M_k\\to M_k$ and a measure $\\mu$ on $M_k$ we define the linear operator $\\phi_L:M_k \\to M_k$, by the law $\\rho \\,\\to\\,\\phi_L(\\rho) = \\int_{M_k} L(v) \\rho L(v)^\\dagger \\, \\dm(v).$\n  On a previous work the authors show that for a fixed measure $\\mu$ it is generic on the function $L$ the $\\Phi$-Erg property (also irreducibility). Here we will show that the purification property is also generic on $L$ for a fixed $\\mu$.\n  Given $L$ and $\\mu$ there"},"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":"1908.08942","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-22T23:14:50Z","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"title_canon_sha256":"9547182a6bd695338fdb7d36aaa7ad1417147039ed15bdb89e634b2ab9c9651b","abstract_canon_sha256":"13246d76d83dc6bc23ea24a114dcd960a1f9374d8a638fd7405e351fec335766"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:14:31.526341Z","signature_b64":"Sr8NsKQt3h0tYc5geiZiZSgc8RnTdmvd6U7Ym0duicrQt+np6iVyHKRLvCZG3p2qREo2BSPuI2MmYZJc5McSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0e83881800cc435e8e30ca5fe7ea2bf2f98bba0d43e697fb2b050f19c1b9497","last_reissued_at":"2026-07-05T03:14:31.525841Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:14:31.525841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lyapunov exponents for Quantum Channels: an entropy formula and generic properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","quant-ph"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Jader E. Brasil, Josue Knorst","submitted_at":"2019-08-22T23:14:50Z","abstract_excerpt":"We denote by $M_k$ the set of $k$ by $k$ matrices with complex entries. We consider quantum channels $\\phi_L$ of the form: given a measurable function $L:M_k\\to M_k$ and a measure $\\mu$ on $M_k$ we define the linear operator $\\phi_L:M_k \\to M_k$, by the law $\\rho \\,\\to\\,\\phi_L(\\rho) = \\int_{M_k} L(v) \\rho L(v)^\\dagger \\, \\dm(v).$\n  On a previous work the authors show that for a fixed measure $\\mu$ it is generic on the function $L$ the $\\Phi$-Erg property (also irreducibility). Here we will show that the purification property is also generic on $L$ for a fixed $\\mu$.\n  Given $L$ and $\\mu$ there"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08942","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08942/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.08942","created_at":"2026-07-05T03:14:31.525907+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.08942v3","created_at":"2026-07-05T03:14:31.525907+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08942","created_at":"2026-07-05T03:14:31.525907+00:00"},{"alias_kind":"pith_short_12","alias_value":"4DUDRAMABTCD","created_at":"2026-07-05T03:14:31.525907+00:00"},{"alias_kind":"pith_short_16","alias_value":"4DUDRAMABTCDL2HD","created_at":"2026-07-05T03:14:31.525907+00:00"},{"alias_kind":"pith_short_8","alias_value":"4DUDRAMA","created_at":"2026-07-05T03:14:31.525907+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/4DUDRAMABTCDL2HDBSS747VCX4","json":"https://pith.science/pith/4DUDRAMABTCDL2HDBSS747VCX4.json","graph_json":"https://pith.science/api/pith-number/4DUDRAMABTCDL2HDBSS747VCX4/graph.json","events_json":"https://pith.science/api/pith-number/4DUDRAMABTCDL2HDBSS747VCX4/events.json","paper":"https://pith.science/paper/4DUDRAMA"},"agent_actions":{"view_html":"https://pith.science/pith/4DUDRAMABTCDL2HDBSS747VCX4","download_json":"https://pith.science/pith/4DUDRAMABTCDL2HDBSS747VCX4.json","view_paper":"https://pith.science/paper/4DUDRAMA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.08942&json=true","fetch_graph":"https://pith.science/api/pith-number/4DUDRAMABTCDL2HDBSS747VCX4/graph.json","fetch_events":"https://pith.science/api/pith-number/4DUDRAMABTCDL2HDBSS747VCX4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4DUDRAMABTCDL2HDBSS747VCX4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4DUDRAMABTCDL2HDBSS747VCX4/action/storage_attestation","attest_author":"https://pith.science/pith/4DUDRAMABTCDL2HDBSS747VCX4/action/author_attestation","sign_citation":"https://pith.science/pith/4DUDRAMABTCDL2HDBSS747VCX4/action/citation_signature","submit_replication":"https://pith.science/pith/4DUDRAMABTCDL2HDBSS747VCX4/action/replication_record"}},"created_at":"2026-07-05T03:14:31.525907+00:00","updated_at":"2026-07-05T03:14:31.525907+00:00"}