{"paper":{"title":"Online Shadow Tomography Matching the Classical Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"Angelos Pelecanos, John Wright, Ryan O'Donnell, Sitan Chen","submitted_at":"2026-07-31T17:59:54Z","abstract_excerpt":"In \\emph{Online Shadow Tomography}, we are given copies of an unknown $d$-dimensional quantum state $\\rho$, an adversary (adaptively) proposes a sequence of bounded observables $A^{(1)},\\ldots,A^{(m)}$, and after each $A^{(t)}$ is given we must estimate $\\Tr(A^{(t)}\\rho)$ to within $\\pm \\epsilon$.\n  This is the direct quantum generalization of the classical problem of \\emph{Adaptive Data Analysis}. %The ``offline'' case, in which $A^{(1)}, \\ldots, A^{(m)}$ are given upfront, is also a well-studied problem. The main goal is to minimize the number of copies, $n$, required.\n  Prior results for on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29686","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/2607.29686/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"}