{"paper":{"title":"Measuring Quantum Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Aaron B. Wagner, Ibrahim Issa, Jayadev Acharya, Nirmal V. Shende","submitted_at":"2017-11-02T16:53:17Z","abstract_excerpt":"The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of measuring the von Neumann entropy, $S(\\rho)$, and R\\'enyi entropy, $S_\\alpha(\\rho)$ of an unknown mixed quantum state $\\rho$ in $d$ dimensions, given access to independent copies of $\\rho$.\n  We provide an algorithm with copy complexity $O(d^{2/\\alpha})$ for estimating $S_\\alpha(\\rho)$ for $\\alpha<1$, and copy complexity $O(d^{2})$ for estimating $S(\\rho)$, and $S_\\alpha(\\rho)$ for non-integral $\\alpha>1$. These bounds are at least quadratic in $d$, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00814","kind":"arxiv","version":2},"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/1711.00814/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"}