Delocalization of quantum information in long-range interacting systems

TL;DR

This paper studies how quantum information spreads and localizes in long-range interacting spin chains, revealing regimes where information is globally delocalized or accessible locally, with implications for quantum correlations and entanglement.

Contribution

It introduces the use of tripartite mutual information to distinguish different information propagation regimes in long-range systems, highlighting the role of interaction decay rate.

Findings

Fast decay interactions lead to global delocalization of information.

Slow decay interactions allow quasi-instantaneous information propagation.

Quantum entanglement dominates correlations in certain regimes.

Abstract

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), whose sign 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 behaviour 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 apart from entanglement, other nonmonogamous correlations are sizeable 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.