{"paper":{"title":"Determination of all pure quantum states from a minimal number of observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Damien Mondragon, Vladislav Voroninski","submitted_at":"2013-06-05T19:38:23Z","abstract_excerpt":"We show that for any positive integer $n$, the maps $x \\in \\mathbb{C}^n \\mapsto \\{\\left|\\langle x, z_i \\rangle \\right|^2\\}_{i=1}^{4n} \\in \\mathbb{R}^{4n}$, where $z_i$ are the columns of four $n\\times n$ unitary matrices, are generically injective modulo multiplication by a global phase factor, yielding a family of embeddings of $\\mathbb{C}P^{n-1}$ into $\\mathbb{R}^{4n-4}$. In particular, this implies that distribution measurements about a pure state with four generic full-rank observables are informationally complete, which is sharp for $n \\geq 6$. To complement this information-theoretic stu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1214","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"}