{"paper":{"title":"Estimating Fidelity to a Reference Quantum State","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Qisheng Wang","submitted_at":"2026-06-24T17:09:20Z","abstract_excerpt":"We consider the problem of estimating the fidelity of an unknown quantum state to a known reference state to within additive error $\\varepsilon$. We show that the sample complexity is $O(r^2/\\varepsilon^2)$ with optimal $\\varepsilon$-dependence when the reference state is of rank $r$, improving the previous best $O(r^2\\log^2(1/\\varepsilon)/\\varepsilon^4)$ due to Utsumi, Nakata, Wang, and Takagi (QIP 2026). We also provide a lower bound of $\\Omega(r/\\varepsilon^2)$, improving the previous best $\\Omega(r/\\varepsilon+1/\\varepsilon^2)$, with implications to quantum query complexity. Moreover, we f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26034","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/2606.26034/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"}