  Quantum field theory defined on a noncommutative space is a useful toy model
of quantum gravity and is known to have several intriguing properties, such as
nonlocality and UV/IR mixing. They suggest novel types of correlation among the
degrees of freedom of different energy scales. In this paper, we investigate
such correlations by the use of entanglement entropy in the momentum space. We
explicitly evaluate the entanglement entropy of scalar field theory on a fuzzy
sphere and find that it exhibits different behaviors from that on the usual
continuous sphere. We argue that these differences would originate in different
characteristics; non-planar contributions and matrix regularization. It is also
found that the mutual information between the low and the high momentum modes
shows different scaling behaviors when the effect of a cutoff becomes
important.
