Generalized Symmetries and Entanglement in Quantum Field Theory

This thesis studies two quantum-information quantities in theories with generalized symmetries: entanglement asymmetry, which measures symmetry breaking, and symmetry-resolved entanglement entropy, which decomposes entanglement into symmetry sectors. Generalized symmetries are described by topological defects and include ordinary group, higher-form, and noninvertible symmetries. In this setting, both quantities must be defined with respect to the algebra of symmetry operators acting on the Hilbert space under consideration. In two spacetime dimensions, this may be the fusion or tube algebra on a circle, depending on whether twisted sectors are included, or the strip algebra on an interval. The interval case also depends on the boundary conditions introduced at the entangling surface; since anomalies constrain the available boundary conditions, they can affect the subsystem symmetry algebra and its representations. The first work presented here develops entanglement asymmetry for generalized symmetries by constructing a unique universal symmetrizer for strongly separable algebras and applying it to fusion, tube, and strip algebras. The second constructs symmetry-resolved entanglement entropy in the presence of anomalous and noninvertible symmetries, showing through several examples how the allowed entangling boundaries affect sector probabilities and entanglement equipartition. Several technical appendices provide some categorical and algebraic background, as well as detailed constructions and proofs.