{"paper":{"title":"Estimation of low rank density matrices: bounds in Schatten norms and other distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Dong Xia, Vladimir Koltchinskii","submitted_at":"2016-04-15T18:56:35Z","abstract_excerpt":"Let ${\\mathcal S}_m$ be the set of all $m\\times m$ density matrices (Hermitian positively semi-definite matrices of unit trace). Consider a problem of estimation of an unknown density matrix $\\rho\\in {\\mathcal S}_m$ based on outcomes of $n$ measurements of observables $X_1,\\dots, X_n\\in {\\mathbb H}_m$ (${\\mathbb H}_m$ being the space of $m\\times m$ Hermitian matrices) for a quantum system identically prepared $n$ times in state $\\rho.$ Outcomes $Y_1,\\dots, Y_n$ of such measurements could be described by a trace regression model in which ${\\mathbb E}_{\\rho}(Y_j|X_j)={\\rm tr}(\\rho X_j), j=1,\\dot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04600","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"}