Scalable Test of Genuine Multipartite Entanglement via Partially Randomized Measurements

Experimental data from the five-qubit GHZ demonstration on the Piast-Q trapped-ion quantum computer. Each row corresponds to one measurement setting and contains the squared correlation function $E^2$ (column \texttt{T2}) together with the five local rotation angles $\theta_i$ of the $R_z(\theta_i)$ gates, which specify the measurement directions within the $xy$ plane. Every correlation was estimated from 200 shots. The file \texttt{GHZ\_standard.csv} contains the $2^{N-1}=16$ settings with $\theta_i \in \{0,\pi/2\}$, corresponding to the nonzero correlation tensor elements in the $xy$ subsector; their sum yields $\|T\|^2_{xy} = 8.55 \pm 0.07$. The file \texttt{GHZ\_random.csv} contains 481 settings with $\theta_i$ drawn uniformly from $(0,2\pi)$; the mean of the squared correlations yields$\mathcal{R}^{(2)}_{xy} = 0.27775 \pm 0.00998$.