## Generalized entanglement entropies of quantum designs

The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to condensed matter to high energy. Ensembles of quantum states or unitaries that reproduce the first t moments of completely random states or unitary channels (drawn from the Haar measure) are called t-designs. Entropic functions of the t-th power of a density operator are called t-entropies (e.g. Renyi and Tsallis).