In recent years, analysis methods for quantum states based on randomized measurements have been investigated extensively. Still, in the experimental implementations these methods were typically used for characterizing strongly entangled states and not to analyze the different families of multiparticle or weakly entangled states. In this work, we experimentally prepare various entangled states with path-polarization hyper-entangled photon pairs, and study their entanglement properties using the full toolbox of randomized measurements. First, we successfully characterize the correlations of a series of GHZ-W mixed states using the second moments of the random outcomes, and demonstrate the advantages of this method by comparing it with the well-known three-tangle and squared concurrence. Second, we generate bound entangled chessboard states of two three-dimensional systems and verify their weak entanglement with a criterion derived from moments of randomized measurements.
@article{arxiv.2307.04382,
title = {Experimental verification of bound and multiparticle entanglement with the randomized measurement toolbox},
author = {Chao Zhang and Yuan-Yuan Zhao and Nikolai Wyderka and Satoya Imai and Andreas Ketterer and Ning-Ning Wang and Kai Xu and Keren Li and Bi-Heng Liu and Yun-Feng Huang and Chuan-Feng Li and Guang-Can Guo and Otfried Gühne},
journal= {arXiv preprint arXiv:2307.04382},
year = {2023}
}