{"paper":{"title":"Quantum state certification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"Costin B\\u{a}descu, John Wright, Ryan O'Donnell","submitted_at":"2017-08-20T18:41:41Z","abstract_excerpt":"We consider the problem of quantum state certification, where one is given $n$ copies of an unknown $d$-dimensional quantum mixed state $\\rho$, and one wants to test whether $\\rho$ is equal to some known mixed state $\\sigma$ or else is $\\epsilon$-far from $\\sigma$. The goal is to use notably fewer copies than the $\\Omega(d^2)$ needed for full tomography on $\\rho$ (i.e., density estimation). We give two robust state certification algorithms: one with respect to fidelity using $n = O(d/\\epsilon)$ copies, and one with respect to trace distance using $n = O(d/\\epsilon^2)$ copies. The latter algori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06002","kind":"arxiv","version":3},"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"}