We review various bounds concerning out-of-equilibrium dynamics in few-level and many-
body quantum systems. We primarily focus on closed quantum systems but will also mention …

A wave function subject to unitary time evolution and exposed to measurements undergoes
pure state dynamics, with deterministic unitary and probabilistic measurement-induced state …

Scrambling processes, which rapidly spread entanglement through many-body quantum
systems, are difficult to investigate using standard techniques, but are relevant to quantum …

We show that out-of-time-order correlators (OTOCs) constitute a probe for local-operator
entanglement (LOE). There is strong evidence that a volumetric growth of LOE is a faithful …

This tutorial article introduces the physics of quantum information scrambling in quantum
many-body systems. The goals are to understand how to precisely quantify the spreading of …

Dual-unitary quantum circuits can be used to construct 1+ 1 dimensional lattice models for
which dynamical correlations of local observables can be explicitly calculated. We show …

Quantum thermalization in a many-body system is defined by the approach of local
subsystems toward a universal form, describable as an ensemble of quantum states wherein …

We study the out-of-equilibrium dynamics of the quantum cellular automaton known as “Rule
54.” For a class of low-entangled initial states, we provide an analytic description of the effect …

The concept of space evolution (or space-time duality) has emerged as a promising
approach for studying quantum dynamics. The basic idea involves exchanging the roles of …

We study the spreading of quantum information in a recently introduced family of brickwork
quantum circuits that generalizes the dual-unitary class. These circuits are unitary in time …