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We investigate the delocalization of quantum information in thenonequilibrium dynamics of the $XY$ spin chain with asymptotically decayinginteractions $\sim 1/r^{\alpha}$. As a figure of merit, we employ thetripartite mutual information (TMI), whose sign indicates if quantuminformation is predominantly shared globally. Interestingly, the sign of theTMI distinguishes regimes of the exponent $\alpha$ that are known for differentbehaviour of information propagation. While an effective causal region boundsthe propagation of information, if interactions decay sufficiently fast, thisinformation is mainly delocalized, which leads to the necessity of globalmeasurements. Furthermore, the results indicate that mutual information ismonogamous for all possible partitionings in this case, implying that quantumentanglement is the dominant correlation. If interactions decay sufficientlyslow, though information can propagate (quasi-)instantaneously, it is mainlyaccessible by local measurements at early times. Furthermore, it takes somefinite time until correlations start to become monogamous, which suggests thatapart from entanglement, other nonmonogamous correlations are sizeable at earlytimes. Our findings give new insights into the dynamics, and structure ofquantum information in many-body systems with long-range interactions, andmight get verified on state-of-the-art experimental platforms.

Delocalization of quantum information in long-range interacting systems