基于随机测量的多粒子量子关联的统计显著性检验
Statistically significant tests of multiparticle quantum correlations based on randomized measurements
AI总结：
该研究提出基于局部随机测量有限样本的多量子比特判据层级，利用二阶矩和大偏差界评估统计显著性，从而认证中等规模量子系统中的多粒子纠缠并确定所需测量资源。
摘要：
我们考虑基于局部随机测量的有限样本的统计方法，以认证中等规模量子系统中不同程度的多粒子纠缠。我们首先引入多量子比特判据的层级结构，这些判据由关于不同大小划分可分的态所满足，并且只涉及基础概率分布的二阶矩。随后，我们详细分析实验中估计的统计误差，并提出若干基于大偏差界来估计统计显著性的方法。后者使我们能够表征认证多粒子关联所需的测量资源，并详细分析给定的实验数据。
英文摘要：
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of multi-qubit criteria, satisfied by states which are separable with respect to partitions of different size, involving only second moments of the underlying probability distribution. Then, we analyze in detail the statistical error of the estimation in experiments and present several approaches for estimating the statistical significance based on large deviation bounds. The latter allows us to characterize the measurement resources required for the certification of multiparticle correlations, as well as to analyze given experimental data in detail.
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