We investigate the delocalization of quantum information in the nonequilibrium dynamics of the $XY$ spin chain with asymptotically decaying interactions $\sim 1/r^{\alpha }$. As a figure of merit, we employ the tripartite mutual information (TMI), the sign of which indicates if quantum information is predominantly shared globally. Interestingly, the sign of the TMI distinguishes regimes of the exponent $\alpha$ that are known for different behaviors of information propagation. While an effective causal region bounds the propagation of information, if interactions decay sufficiently fast, this information is mainly delocalized, which leads to the necessity of global measurements. Furthermore, the results indicate that mutual information is monogamous for all possible partitionings in this case, implying that quantum entanglement is the dominant correlation. If interactions decay sufficiently slow, though information can propagate (quasi-)instantaneously, it is mainly accessible by local measurements at early times. Furthermore, it takes some finite time until correlations start to become monogamous, which suggests that entanglement is not the dominant correlation at early times. Our findings give new insights into the dynamics and structure of quantum information in many-body systems with long-range interactions, and might get verified on state-of-the-art experimental platforms.

• Received 14 May 2021
• Accepted 31 August 2021

DOI:https://doi.org/10.1103/PhysRevA.104.042409