{"paper":{"title":"Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Emmanuel J. Candes, Xiaodong Li","submitted_at":"2012-08-30T17:53:05Z","abstract_excerpt":"This note shows that we can recover a complex vector x in C^n exactly from on the order of n quadratic equations of the form |<a_i, x>|^2 = b_i, i = 1, ..., m, by using a semidefinite program known as PhaseLift. This improves upon earlier bounds in [3], which required the number of equations to be at least on the order of n log n. We also demonstrate optimal recovery results from noisy quadratic measurements; these results are much sharper than previously known results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6247","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"}