{"paper":{"title":"On estimating Schatten norm and power distances between quantum states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Qisheng Wang, Yupan Liu","submitted_at":"2025-05-01T11:15:20Z","abstract_excerpt":"We study the computational complexity of estimating the quantum Schatten $\\alpha$-norm distance ${\\rm T}_\\alpha(\\rho_0,\\rho_1)$, given ${\\rm poly}(n)$-size state-preparation circuits of $n$-qubit quantum states $\\rho_0$ and $\\rho_1$. This quantity serves as a lower bound on the trace distance and, for $\\alpha > 1$, is interchangeable with its powered version $\\Lambda_\\alpha(\\rho_0,\\rho_1)$. For any constant $\\alpha > 1$, we develop an efficient rank-independent quantum estimator for ${\\rm T}_\\alpha(\\rho_0,\\rho_1)$ with time complexity ${\\rm poly}(n)$, achieving an exponential speedup over the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00457","kind":"arxiv","version":3},"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/2505.00457/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"}