{"paper":{"title":"Nonasymptotic bounds for quantum purity amplification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jack Spilecki, John Wright, Thilo Scharnhorst","submitted_at":"2026-05-26T16:39:24Z","abstract_excerpt":"In quantum purity amplification, one is given $n$ copies of a noisy quantum state $\\rho \\in \\mathbb{C}^{d \\times d}$ and asked to prepare $k$ copies of its principal eigenstate $|v_d\\rangle$. Several prior works have derived information-theoretically optimal algorithms for this problem, but the bounds they prove are only shown in the asymptotic regime as the number of samples $n$ tends to infinity. In this paper, we establish the following nonasymptotic guarantee: if $\\rho$'s eigenvalues are sorted $p_1 \\leq \\cdots \\leq p_d$ and $p_{d-1} < p_d$, then \\begin{equation*}\n  n = O\\Big(k + \\frac{k}{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27262","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.27262/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}