{"paper":{"title":"Pure state `really' informationally complete with rank-1 POVM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Yun Shang, Yu Wang","submitted_at":"2017-11-21T00:25:38Z","abstract_excerpt":"What is the minimal number of elements in a rank-1 positive-operator-valued measure (POVM) which can uniquely determine any pure state in $d$-dimensional Hilbert space $\\mathcal{H}_d$? The known result is that the number is no less than $3d-2$. We show that this lower bound is not tight except for $d=2$ or 4. Then we give an upper bound of $4d-3$. For $d=2$, many rank-1 POVMs with four elements can determine any pure states in $\\mathcal{H}_2$. For $d=3$, we show eight is the minimal number by construction. For $d=4$, the minimal number is in the set of $\\{10,11,12,13\\}$. We show that if this n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07585","kind":"arxiv","version":1},"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"}