{"paper":{"title":"Optimal estimation of high-dimensional quantum states using locally gentle measurements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph","stat.TH"],"primary_cat":"math.ST","authors_text":"Cristina Butucea, Henning Stein, Jan Johannes","submitted_at":"2026-07-27T14:28:07Z","abstract_excerpt":"We study the task of estimating a $d-$dimensional quantum state $\\rho$ under the constraint that the measurement is $\\alpha-$gentle. Such measurements $M$ do not collapse the state; they issue both a random variable $R^M = \\omega$ containing statistical information and a post-measurement state $\\rho_{M \\to \\omega}$ such that $\\|\\rho_{M\\to \\omega} - \\rho\\|_{Tr} \\leq \\alpha$. We describe gentle measurements and their connection to quantum differential privacy.\n  Our results show that the optimal minimax estimation rate in Frobenius norm is of order $d^3/(n \\alpha^2)$, instead of $d^2/n$ for gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24491","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/2607.24491/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"}