arXiv:1405.6471v1 [hep-th] 26 May 2014 Quantum Entropy for Fuzzy sphere S 2 F and Monopoles on S 2 F Nirmalendu Acharyya ∗ a , Nitin Chandra † b , and Sachindeo Vaidya ‡ a a Centre for High Energy Physics, Indian Institute of Science, Bangalore-560012, India b The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai-600113, India Abstract Using generalized bosons, we construct the fuzzy sphere S 2 F and monopoles on S 2 F 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 non-abelian unitary gauge symmetry which is in the commu- tant 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. * nirmalendu@cts.iisc.ernet.in † nitinc@imsc.res.in ‡ vaidya@cts.iisc.ernet.in 1