发表机构
Syracuse University; Institute for Quantum & Information Sciences, Syracuse University; University of Waterloo; Institute for Quantum Computing, University of Waterloo（雪城大学; 雪城大学量子与信息科学研究所; 滑铁卢大学; 滑铁卢大学量子计算研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立协变量子态层析协议分析框架，推导多种协议的速率函数并证明其严格排序，进而得出Wasserstein型样本复杂度的严格不等式，表明速率函数是比样本复杂度更精细的性能指标。
AI 中文摘要
量子态层析协议可以通过其样本复杂度或控制误差估计大偏差行为的层析速率函数来表征。我们建立了一个用于分析协变协议的框架，使我们能够比较这些度量。首先，我们推导了几种协议的速率函数，包括基于随机纯化的协议和Haah等人的样本最优协议。这些速率函数用一个新的散度族表示，该族包括反向夹层Rényi散度和Keyl的退火量子相对熵作为特例。我们表明，这些速率函数满足严格排序，尽管每个协议的样本复杂度是阶最优的。我们考虑基于Wasserstein距离而非迹距离的样本复杂度不同版本，并表明速率函数的排序意味着Wasserstein型样本复杂度的类似严格不等式。因此，层析速率函数比通常的样本复杂度更精细地指示层析协议的性能。
英文摘要
Protocols for quantum state tomography can be characterized either by their sample complexity or by the tomographic rate function that governs the large deviation behaviour of error estimates. We establish a framework for the analysis of covariant protocols which allows us to compare these measures. First, we derive the rate functions for several protocols, including random purification-based protocols and the sample-optimal protocol of Haah et al. These rate functions are expressed in terms of a new family of divergences which includes the reverse sandwiched Rényi divergence and Keyl's annealed quantum relative entropy as special cases. We show that these rate functions obey a strict ordering, even though the sample complexity of each protocol is order optimal. We consider a different version of sample complexity based on Wasserstein distance rather than trace distance, and show that the ordering of the rate functions implies analogous strict inequalities for the Wasserstein-type sample complexity. Thus the tomographic rate function is a more fine-grained indicator of the performance of a tomography protocol than the usual sample complexity.
Comments36 pages, 2 figures
