2026-10-15 · arXiv Quantum Physics
arXiv:2610.19936v1 Announce Type: new
Abstract: Entropy estimation of discrete probability distributions is a fundamental problem in statistical inference and quantum property estimation. In this paper, we study the problem of estimating R\'enyi entropy $H_\alpha(\mathbf{p})$ for any distribution $\mathbf{p} = (p_i)_{i=1}^n$ given its purified quantum query-access. For non-integer $\alpha 1$, our algorithm estimates $H_\alpha(\mathbf{p})$ to within additive error $\epsilon$ using only $\widetilde{\mathcal{O}}\big(n^{\max\{1/2,1-1/\alpha\}}/\epsilon\big)$ queries, which improves the best known upper bound for dependence on both $n$ and $1/\epsilon$. For $0
原文链接：https://arxiv.org/abs/2610.19936
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