{"paper":{"title":"Simultaneous Estimation of Nonlinear Functionals of a Quantum State","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kean Chen, Qisheng Wang, Zhan Yu, Zhicheng Zhang","submitted_at":"2025-05-22T14:23:48Z","abstract_excerpt":"We consider a fundamental task in quantum information theory, estimating the values of $\\operatorname{tr}(O\\rho)$, $\\operatorname{tr}(O\\rho^2)$, ..., $\\operatorname{tr}(O\\rho^k)$ for an observable $O$ and a quantum state $\\rho$. We show that $\\widetilde\\Theta(k)$ samples of $\\rho$ are sufficient and necessary to simultaneously estimate all the $k$ values. This means that estimating all the $k$ values is almost as easy as estimating only one of them, $\\operatorname{tr}(O\\rho^k)$. As an application, our approach advances the sample complexity of entanglement spectroscopy and the virtual cooling "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16715","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/2505.16715/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"}