Quantum information in conformal field theory

In this talk we consider different problems related to the dynamics of quantum information in systems described by conformal quantum field theory. For such systems, we will discuss the properties of various quantum measures of entanglement, such as the entanglement entropy, the entanglement contour, the properties of the modular Hamiltonian and their possible generalizations, as well as their behavior in various nonequilibrium states. Also we will briefly discuss some modern problems about the interrelation between two-dimensional conformal field theory and three-dimensional gravity.