Quantum entropy for the fuzzy sphere and its monopoles

Using generalized bosons, we construct the fuzzy sphere S-F(2) and monopoles on S-F(2) in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.