Experimental Detection of the Correlation R ́enyi Entropy in the Central Spin Model.

Abstract

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 of a central spin coupled and initially uncorrelated with 15 other spins. Due to the spin-spin interactions, information flows from the central spin to the surrounding ones forming clusters of multi-spin correlations that grow in time. We design a nuclear magnetic resonance experiment that directly measures the amplitudes of the multi-spin correlations and use them to compute the evolution of what we call correlation R ́enyi entropy. This entropy keeps growing even after the equilibration of the entanglement entropy. We also analyze how the saturation point and the timescale for the equilibration of the correlation R ́enyi entropy depend on the system size