Statistically significant tests of multiparticle quantum correlations based on randomized measurements

TL;DR

This paper develops statistical methods using randomized measurements to certify multiparticle entanglement in quantum systems, providing hierarchies of criteria, analyzing statistical errors, and estimating measurement resources needed.

Contribution

It introduces new hierarchies of multiparticle entanglement criteria based on second moments and analyzes statistical errors for experimental certification.

Findings

Hierarchies of criteria for multiparticle entanglement

Methods for estimating statistical significance in experiments

Analysis of measurement resources for certification

Abstract

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.