{"paper":{"title":"Breaking the Quadratic Barrier for von Neumann Entropy Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Minbo Gao, Qisheng Wang","submitted_at":"2026-08-11T17:10:34Z","abstract_excerpt":"We study the sample complexity of estimating the von Neumann entropy of an unknown $d$-dimensional quantum state. All previously known estimators require $\\Omega(d^2)$ samples, and plug-in estimators are known to face a quadratic barrier. We give the first subquadratic-sample estimator: for additive error $\\varepsilon$, our estimator uses\n  \\[\n  O\\!\\left(\\frac{d^2 \\log^2(\\log(d)) \\log(1/\\varepsilon)}{\\varepsilon^2 \\log^2(d)} + \\frac{\\log^2(d/\\varepsilon)}{\\varepsilon^2}\\right)\n  \\] samples. In particular, for constant $\\varepsilon$, the complexity is $O_\\varepsilon(d^2\\log^2(\\log(d))/\\log^2(d)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11151","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/2608.11151/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"}