The spectacular development of quantum over the past few years has sparked renewed interest in quantum information. In addition to quantum computation, recent advances permit to envision revolutionary technological developments in quantum simulation, quantum metrology, and quantum communications. Still, many fundamental questions remain unanswered regarding the very foundations of quantum information, first and foremost in connection to quantum correlations and entanglement. This project aims to explore two aspects of these questions: (i) The role of entanglement in quantum phase transitions; (ii) The propagation of information in correlated quantum systems. The roles of disorder and coupling to the environment. Both are fundamental challenges for real quantum devices. We will focus on long-range models as realized on state-of-the-art quantum simulation platforms, including Rydberg atoms, eg as realized at Institut d'Optique, and cavity optical tweezers, eg as realized at the Laboratoire Kastler-Brossel. The challenges are to understand the behavior of quantum information in these systems and to determine the relevant observables to unveil its nature. These questions will be addressed from a theoretical point of view, using the most modern N-body approaches, both analytical and numerical.