{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JQZ4BTMOTJNSVRGM5PATBMCZSK","short_pith_number":"pith:JQZ4BTMO","schema_version":"1.0","canonical_sha256":"4c33c0cd8e9a5b2ac4ccebc130b0599283ac1b98a0409b445ec85b4bc6b4b30c","source":{"kind":"arxiv","id":"1807.01266","version":2},"attestation_state":"computed","paper":{"title":"When Do Composed Maps Become Entanglement Breaking?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Alexander M\\\"uller-Hermes, Matthias Christandl, Michael M. Wolf","submitted_at":"2018-07-03T16:25:59Z","abstract_excerpt":"For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with respect to any qubit ancilla, then applying it to part of a bipartite quantum state will result in a Schmidt number bounded away from the maximum possible value. Iterating this result puts a successively decreasing upper bound on the Schmidt number arising in this way from compositions of such a map. By applying this technique to completely positive maps in d"},"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":"1807.01266","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-03T16:25:59Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.OA"],"title_canon_sha256":"2d9cb62e58e43611c81ed99e54692f05bcd7485514352f1e510c2c999febb4f4","abstract_canon_sha256":"d16b8435d3e5546895343b719069abc03d230d32a342ea95d9afb85f0f945a3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:17.865057Z","signature_b64":"IpEbXN2MNoR3wpULp1TM1arVU1vjNKzPqZ3Rhxd4W9DLB+yEatSYcTubimfPJsJUk5KUASXFyaq/X7+Mi7YeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c33c0cd8e9a5b2ac4ccebc130b0599283ac1b98a0409b445ec85b4bc6b4b30c","last_reissued_at":"2026-05-17T23:43:17.864296Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:17.864296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When Do Composed Maps Become Entanglement Breaking?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Alexander M\\\"uller-Hermes, Matthias Christandl, Michael M. Wolf","submitted_at":"2018-07-03T16:25:59Z","abstract_excerpt":"For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with respect to any qubit ancilla, then applying it to part of a bipartite quantum state will result in a Schmidt number bounded away from the maximum possible value. Iterating this result puts a successively decreasing upper bound on the Schmidt number arising in this way from compositions of such a map. By applying this technique to completely positive maps in d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01266","kind":"arxiv","version":2},"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":"1807.01266","created_at":"2026-05-17T23:43:17.864433+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.01266v2","created_at":"2026-05-17T23:43:17.864433+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01266","created_at":"2026-05-17T23:43:17.864433+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQZ4BTMOTJNS","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQZ4BTMOTJNSVRGM","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQZ4BTMO","created_at":"2026-05-18T12:32:31.084164+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/JQZ4BTMOTJNSVRGM5PATBMCZSK","json":"https://pith.science/pith/JQZ4BTMOTJNSVRGM5PATBMCZSK.json","graph_json":"https://pith.science/api/pith-number/JQZ4BTMOTJNSVRGM5PATBMCZSK/graph.json","events_json":"https://pith.science/api/pith-number/JQZ4BTMOTJNSVRGM5PATBMCZSK/events.json","paper":"https://pith.science/paper/JQZ4BTMO"},"agent_actions":{"view_html":"https://pith.science/pith/JQZ4BTMOTJNSVRGM5PATBMCZSK","download_json":"https://pith.science/pith/JQZ4BTMOTJNSVRGM5PATBMCZSK.json","view_paper":"https://pith.science/paper/JQZ4BTMO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.01266&json=true","fetch_graph":"https://pith.science/api/pith-number/JQZ4BTMOTJNSVRGM5PATBMCZSK/graph.json","fetch_events":"https://pith.science/api/pith-number/JQZ4BTMOTJNSVRGM5PATBMCZSK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQZ4BTMOTJNSVRGM5PATBMCZSK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQZ4BTMOTJNSVRGM5PATBMCZSK/action/storage_attestation","attest_author":"https://pith.science/pith/JQZ4BTMOTJNSVRGM5PATBMCZSK/action/author_attestation","sign_citation":"https://pith.science/pith/JQZ4BTMOTJNSVRGM5PATBMCZSK/action/citation_signature","submit_replication":"https://pith.science/pith/JQZ4BTMOTJNSVRGM5PATBMCZSK/action/replication_record"}},"created_at":"2026-05-17T23:43:17.864433+00:00","updated_at":"2026-05-17T23:43:17.864433+00:00"}