Explore entanglement entropy in conformal field theories featuring non-invertible symmetries through this specialized physics lecture delivered as part of ICTP-SAIFR's comprehensive program on Anomalies, Topology and Quantum Information in Field Theory and Condensed Matter Physics. Delve into the intricate mathematical framework connecting quantum information theory with advanced field theory concepts, examining how non-invertible symmetries affect entanglement measures in conformal field theories. Learn from Javier Molina Vilaplana of Universidad Politécnica de Cartagena as he presents cutting-edge research at the intersection of quantum information and theoretical physics, providing insights into the fundamental relationships between symmetry structures and quantum entanglement properties in conformal systems.