{"paper":{"title":"Efficient quantum tomography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"John Wright, Ryan O'Donnell","submitted_at":"2015-08-08T13:56:26Z","abstract_excerpt":"In the quantum state tomography problem, one wishes to estimate an unknown $d$-dimensional mixed quantum state $\\rho$, given few copies. We show that $O(d/\\epsilon)$ copies suffice to obtain an estimate $\\hat{\\rho}$ that satisfies $\\|\\hat{\\rho} - \\rho\\|_F^2 \\leq \\epsilon$ (with high probability). An immediate consequence is that $O(\\mathrm{rank}(\\rho) \\cdot d/\\epsilon^2) \\leq O(d^2/\\epsilon^2)$ copies suffice to obtain an $\\epsilon$-accurate estimate in the standard trace distance. This improves on the best known prior result of $O(d^3/\\epsilon^2)$ copies for full tomography, and even on the b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01907","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"}