Experimental Detection of the Correlation Rényi Entropy in the Central Spin Model

We propose and experimentally measure an entropy that quantifies the volume of correlations among qubits. The experiment is carried out on a nearly isolated quantum system composed central spin coupled initially uncorrelated with 15 other spins. Due to spin-spin interactions, information flows from surrounding ones forming clusters multi-spin grow in time. design nuclear magnetic resonance directly measures amplitudes use them compute evolution what we call correlation R\'enyi entropy. This keeps growing even after equilibration entanglement also analyze how saturation point timescale for depend size.