{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LIFIJYWCVZZZSSNLDHM7L4ZR56","short_pith_number":"pith:LIFIJYWC","schema_version":"1.0","canonical_sha256":"5a0a84e2c2ae739949ab19d9f5f331efb07efb83c0f0ea83f7dfa39f1112b8aa","source":{"kind":"arxiv","id":"1510.08887","version":3},"attestation_state":"computed","paper":{"title":"Phase Retrieval Using Unitary 2-Designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"quant-ph","authors_text":"Shelby Kimmel, Yi-Kai Liu","submitted_at":"2015-10-29T20:24:21Z","abstract_excerpt":"We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |Tr(C*U)|^2 with unitary matrices C that are chosen by the observer. This problem has applications to quantum process tomography, when the unknown process is a unitary operation.\n  We show that PhaseLift, a convex programming algorithm for phase retrieval, can be adapted to this matrix setting, using measurements that are sampled from unitary 4- and 2-designs. In the case of unitary 4-design "},"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":"1510.08887","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-10-29T20:24:21Z","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"title_canon_sha256":"37288b7ec489de548b260d726f1028951ae5a2e1e8181b654435a178f3d9af0a","abstract_canon_sha256":"033eda8ab2760aa78836864125e8e21492ae83c767aaacaf2e8bb51a2e6ba08f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:57.377167Z","signature_b64":"td/ntgFptZ6YADxRYn985O6QZJo32fdFRyqKXVRGttqxm1fewVZ4X6R0B+OkJ+rnvrqLL6zzM5QT/NZYW/ALAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a0a84e2c2ae739949ab19d9f5f331efb07efb83c0f0ea83f7dfa39f1112b8aa","last_reissued_at":"2026-05-18T00:21:57.376408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:57.376408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase Retrieval Using Unitary 2-Designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"quant-ph","authors_text":"Shelby Kimmel, Yi-Kai Liu","submitted_at":"2015-10-29T20:24:21Z","abstract_excerpt":"We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |Tr(C*U)|^2 with unitary matrices C that are chosen by the observer. This problem has applications to quantum process tomography, when the unknown process is a unitary operation.\n  We show that PhaseLift, a convex programming algorithm for phase retrieval, can be adapted to this matrix setting, using measurements that are sampled from unitary 4- and 2-designs. In the case of unitary 4-design "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08887","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":"1510.08887","created_at":"2026-05-18T00:21:57.376534+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.08887v3","created_at":"2026-05-18T00:21:57.376534+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08887","created_at":"2026-05-18T00:21:57.376534+00:00"},{"alias_kind":"pith_short_12","alias_value":"LIFIJYWCVZZZ","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LIFIJYWCVZZZSSNL","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LIFIJYWC","created_at":"2026-05-18T12:29:29.992203+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/LIFIJYWCVZZZSSNLDHM7L4ZR56","json":"https://pith.science/pith/LIFIJYWCVZZZSSNLDHM7L4ZR56.json","graph_json":"https://pith.science/api/pith-number/LIFIJYWCVZZZSSNLDHM7L4ZR56/graph.json","events_json":"https://pith.science/api/pith-number/LIFIJYWCVZZZSSNLDHM7L4ZR56/events.json","paper":"https://pith.science/paper/LIFIJYWC"},"agent_actions":{"view_html":"https://pith.science/pith/LIFIJYWCVZZZSSNLDHM7L4ZR56","download_json":"https://pith.science/pith/LIFIJYWCVZZZSSNLDHM7L4ZR56.json","view_paper":"https://pith.science/paper/LIFIJYWC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.08887&json=true","fetch_graph":"https://pith.science/api/pith-number/LIFIJYWCVZZZSSNLDHM7L4ZR56/graph.json","fetch_events":"https://pith.science/api/pith-number/LIFIJYWCVZZZSSNLDHM7L4ZR56/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LIFIJYWCVZZZSSNLDHM7L4ZR56/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LIFIJYWCVZZZSSNLDHM7L4ZR56/action/storage_attestation","attest_author":"https://pith.science/pith/LIFIJYWCVZZZSSNLDHM7L4ZR56/action/author_attestation","sign_citation":"https://pith.science/pith/LIFIJYWCVZZZSSNLDHM7L4ZR56/action/citation_signature","submit_replication":"https://pith.science/pith/LIFIJYWCVZZZSSNLDHM7L4ZR56/action/replication_record"}},"created_at":"2026-05-18T00:21:57.376534+00:00","updated_at":"2026-05-18T00:21:57.376534+00:00"}