Würzburg Seminar on Quantum Field Theory and Gravity

The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum information and thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and conflict with the eigenstate thermalization hypothesis. We quantify the effects of a symmetry's non-Abelian nature--of charges' noncommutation--on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that the noncommuting-charge case has more entanglement. Hence charges' noncommutation can promote entanglement. This result demonstrates a relationship between non-abelian symmetries and entanglement.