面向状态框架势的最优量子估计器
Towards Optimal Quantum Estimators for State Frame Potential
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中文总结 AI 辅助
针对不同访问模型下t阶状态框架势的最优估计问题，确定了查询与通用样本模型的复杂度，提出单拷贝存储估计方法并应用于评估投影态系综的随机性。
中文摘要 AI 辅助
状态框架势是衡量量子态系综逼近Haar随机性程度的标准诊断量。本研究在三种逐步弱化的访问模型下，探讨了估计t阶状态框架势至加性误差ε的问题：（i）多态制备预言机的查询访问、（ii）通用样本访问、（iii）单拷贝样本访问。在查询模型中，我们确定了近最优查询复杂度为$\tilde{\theta}(\frac{\root \text{ } \theta \text{ } }{})$，相比Nakata、Takeuchi、Kliesch和Darmawan（PRX Quantum 2025）的先前最佳结果，在t的依赖关系上实现了二次改进。在通用样本模型中，我们确定了最优样本复杂度为$\theta(\frac{t}{\theta^2})$。在单拷贝样本模型中，我们提出了一种存储并估计的方法，其样本复杂度取决于系综权重的Rényi熵。作为应用，我们使用单拷贝算法评估投影态系综的随机性，其中熵项变为与测量一个子系统相关的观测Rényi熵。
英文摘要
The state frame potential is a standard diagnostic of how closely a quantum state ensemble approximates Haar randomness. In this work, we study the problem of estimating the state frame potential of order $t$ to within additive error $\varepsilon$ under three progressively weaker access models: (i) query access to a multi-state-preparation oracle, (ii) general sample access, and (iii) single-copy sample access. In the query model, we establish a near-optimal query complexity of $\widetildeΘ(\sqrt{t}/\varepsilon)$, yielding a quadratic improvement in the dependence on $t$ over the previous best result of Nakata, Takeuchi, Kliesch, and Darmawan (PRX Quantum 2025). In the general sample model, we establish the optimal sample complexity $Θ(t/\varepsilon^2)$. In the single-copy sample model, we present a store-and-estimate approach whose sample complexity depends on the Rényi entropy of the ensemble weights. As an application, we use the single-copy algorithm to assess the randomness of projected state ensembles, where the entropy term becomes the observational Rényi entropy associated with measuring one subsystem.
