Dynamics of quantum information in many-body systems with nonlocal interactions

The dynamics of quantum information lies at the heart of future technologies that aim to utilize the laws of quantum mechanics for practical purposes. Beyond that, it provides a unifying language that shines new light on longstanding problems home to historically separate fields of theoretical physics. Considering how quantum information propagates and spreads over the degrees of freedom of a quantum many-body system far from equilibrium has proven particularly helpful for various subjects, ranging from the emergence of statistical mechanics in isolated quantum systems to the black hole information paradox. Crucial for these developments are impressive experimental advances that nowadays allow us to explore the nonequilibrium physics of paradigmatic, simple, and (almost) isolated quantum many-body systems in the laboratory. In this thesis, we investigate the dynamics of quantum information in one-dimensional systems of interacting qubits, i.e., spin-chains, where we particularly consider systems that embody nonlocal interactions. The latter are ubiquitous in many experimental platforms for quantum simulation. Our results reveal an interesting connection between two complementary probes of quantum information dynamics, i.e., entanglement growth and operator spreading. This connection allows us to characterize different dynamical classes and underlines that nonlocal interactions induce rich behavior, such as slow thermalization accompanied by superballistic information propagation. In particular, we show that the famous slowdown of entanglement growth in systems with powerlaw interactions implies a slowdown of operator dynamics. The latter clearly distinguishes a system with powerlaw interactions from a system possessing fast scrambling, a characteristic property of black holes and holographic duals to theories of quantum gravity