Symmetry Enforced Entanglement from Projective Non-invertible Symmetry

Explore how projective non-invertible symmetries enforce specific entanglement patterns in quantum systems through this conference talk delivered at ICTP-SAIFR's Program on Anomalies, Topology and Quantum Information in Field Theory and Condensed Matter Physics. Delve into the mathematical framework connecting symmetry principles to quantum entanglement structures, examining how non-invertible symmetries—which cannot be undone by their inverse—create constraints on the possible entanglement configurations in many-body quantum systems. Learn about the projective nature of these symmetries and their implications for understanding quantum phases of matter, topological order, and information-theoretic properties of condensed matter systems. Discover the theoretical foundations that link abstract symmetry concepts to measurable quantum information quantities, providing insights into how fundamental symmetries shape the entanglement landscape in quantum field theories and condensed matter models.