{"paper":{"title":"On estimating operator norm distance, with optimal trace distance estimation when one state is pure","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Qisheng Wang, Yupan Liu, Zhan Yu","submitted_at":"2026-07-04T14:59:03Z","abstract_excerpt":"We investigate the computational complexity of estimating the operator norm distance ${\\rm T}_{\\infty}(\\rho_0,\\rho_1)$, defined via the operator norm $\\|A\\|_{\\infty} = \\sigma_{\\max}(A)$, given ${\\rm poly}(n)$-size state-preparation circuits of $n$-qubit quantum states $\\rho_0$ and $\\rho_1$. We provide efficient quantum estimators for the operator norm distance whose complexity is independent of the rank (and thus the dimension) of the states:\n  1. When one state is pure, we establish an optimal quantum estimator using $\\Theta(1/\\epsilon)$ queries to the state-preparation circuits. Consequently"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03905","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/2607.03905/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"}