In this review recent investigations are summarized of many-body quantum systems with
long-range interactions, which are currently realized in Rydberg atom arrays, dipolar …

We review the mathematical speed limits on quantum information processing in many-body
systems. After the proof of the Lieb–Robinson Theorem in 1972, the past two decades have …

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct
approach to decomposing the exponential of a sum of operators. Despite significant effort …

Continuously monitoring the environment of a quantum many-body system reduces the
entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of …

In ergodic many-body quantum systems, locally encoded quantum information becomes, in
the course of time evolution, inaccessible to local measurements. This concept of …

This work explores a fundamental dynamical structure for a wide range of many-body
quantum systems under periodic driving. Generically, in the thermodynamic limit, such …

Experimental progress in atomic, molecular, and optical platforms in the last decade has
stimulated strong and broad interest in the quantum coherent dynamics of many long-range …

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting
quantum spin models. Effective spins are represented by appropriate internal energy levels …

We study scrambling in connection with multipartite entanglement dynamics in regular and
chaotic long-range spin chains, characterized by a well-defined semi-classical limit. For …

The Lieb-Robinson theorem states that information propagates with a finite velocity in
quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits …