{"paper":{"title":"Instance-optimal high-precision shadow tomography with few-copy measurements: A metrological approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"quant-ph","authors_text":"Senrui Chen, Sisi Zhou, Weiyuan Gong","submitted_at":"2026-02-04T19:00:00Z","abstract_excerpt":"We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $\\rho$ and a known set of observables $\\{O_i\\}_{i=1}^m$, the goal is to estimate expectation values $\\{\\mathrm{tr}(O_i\\rho)\\}_{i=1}^m$ to accuracy $\\epsilon$ in $L_p$-norm, using possibly adaptive measurements that act on $O(\\mathrm{polylog}(d))$ number of copies of $\\rho$ at a time. We focus on the regime where $\\epsilon$ is below an instance-dependent threshold.\n  Our main contribution is an instance-optimal characterization "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04952","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/2602.04952/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"}