{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:6KVRG53CA3D3JWJT5NG2IG7PCB","short_pith_number":"pith:6KVRG53C","schema_version":"1.0","canonical_sha256":"f2ab13776206c7b4d933eb4da41bef105a4edf9f6a5a45a2ecd5b739790202d9","source":{"kind":"arxiv","id":"2510.06909","version":2},"attestation_state":"computed","paper":{"title":"Optimizing LOCC Protocols on Product Stiefel Manifold","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Cheng-Kai Zhu, Xin Wang, Ze-Tong Li","submitted_at":"2025-10-08T11:43:47Z","abstract_excerpt":"Characterizing the operational limits of Local Operations and Classical Communication (LOCC) is a central problem in distributed quantum information, yet remains computationally intractable due to the non-convex geometry of the LOCC set. We introduce a geometric framework that embeds the physical constraints of fixed-round LOCC protocols onto the product Stiefel manifold, converting a constrained protocol-design problem into unconstrained Riemannian optimization. We demonstrate this framework through entanglement distillation: by directly optimizing finite-copy LOCC protocols, we discover achi"},"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":"2510.06909","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-10-08T11:43:47Z","cross_cats_sorted":[],"title_canon_sha256":"5ac04d99aa44ce803c3161fb1ebaf6f5f1f4a51b9cdeac055a136620b97362f9","abstract_canon_sha256":"9f342a2ab5198faeb57f7b6d0650d4b336325cbd1193e15413a3eba994cb37a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:14:58.629683Z","signature_b64":"4OwtrzEiYCXGmGVIBoXgJsqw2l+5s4gkNLShKz+xidWHRC+Ng6b6bMyRxBJ1GPsmOo0DJGG8+dm25W9NLhJECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2ab13776206c7b4d933eb4da41bef105a4edf9f6a5a45a2ecd5b739790202d9","last_reissued_at":"2026-06-24T01:14:58.629211Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:14:58.629211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimizing LOCC Protocols on Product Stiefel Manifold","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Cheng-Kai Zhu, Xin Wang, Ze-Tong Li","submitted_at":"2025-10-08T11:43:47Z","abstract_excerpt":"Characterizing the operational limits of Local Operations and Classical Communication (LOCC) is a central problem in distributed quantum information, yet remains computationally intractable due to the non-convex geometry of the LOCC set. We introduce a geometric framework that embeds the physical constraints of fixed-round LOCC protocols onto the product Stiefel manifold, converting a constrained protocol-design problem into unconstrained Riemannian optimization. We demonstrate this framework through entanglement distillation: by directly optimizing finite-copy LOCC protocols, we discover achi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.06909","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.06909/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":"2510.06909","created_at":"2026-06-24T01:14:58.629270+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.06909v2","created_at":"2026-06-24T01:14:58.629270+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.06909","created_at":"2026-06-24T01:14:58.629270+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KVRG53CA3D3","created_at":"2026-06-24T01:14:58.629270+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KVRG53CA3D3JWJT","created_at":"2026-06-24T01:14:58.629270+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KVRG53C","created_at":"2026-06-24T01:14:58.629270+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/6KVRG53CA3D3JWJT5NG2IG7PCB","json":"https://pith.science/pith/6KVRG53CA3D3JWJT5NG2IG7PCB.json","graph_json":"https://pith.science/api/pith-number/6KVRG53CA3D3JWJT5NG2IG7PCB/graph.json","events_json":"https://pith.science/api/pith-number/6KVRG53CA3D3JWJT5NG2IG7PCB/events.json","paper":"https://pith.science/paper/6KVRG53C"},"agent_actions":{"view_html":"https://pith.science/pith/6KVRG53CA3D3JWJT5NG2IG7PCB","download_json":"https://pith.science/pith/6KVRG53CA3D3JWJT5NG2IG7PCB.json","view_paper":"https://pith.science/paper/6KVRG53C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.06909&json=true","fetch_graph":"https://pith.science/api/pith-number/6KVRG53CA3D3JWJT5NG2IG7PCB/graph.json","fetch_events":"https://pith.science/api/pith-number/6KVRG53CA3D3JWJT5NG2IG7PCB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KVRG53CA3D3JWJT5NG2IG7PCB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KVRG53CA3D3JWJT5NG2IG7PCB/action/storage_attestation","attest_author":"https://pith.science/pith/6KVRG53CA3D3JWJT5NG2IG7PCB/action/author_attestation","sign_citation":"https://pith.science/pith/6KVRG53CA3D3JWJT5NG2IG7PCB/action/citation_signature","submit_replication":"https://pith.science/pith/6KVRG53CA3D3JWJT5NG2IG7PCB/action/replication_record"}},"created_at":"2026-06-24T01:14:58.629270+00:00","updated_at":"2026-06-24T01:14:58.629270+00:00"}