  Classical nonlinear canonical (Poisson) maps have a distinguished role in
quantum mechanics. They act unitarily on the quantum phase space and generate
$\hbar$-independent quantum canonical maps. It is shown that such maps act in
the noncommutative phase space as dictated by the classical covariance. A
crucial observation made is that under the classical covariance the local
quantum mechanical picture can become nonlocal in the Hilbert space. This
nonlocal picture is made equivalent by the Weyl map to a noncommutative picture
in the phase space formulation of the theory. The connection between the
entanglement and nonlocality of the representation is explored and specific
examples of the generation of entanglement are provided by using such concepts
as the generalized Bell states. That the results have direct application in
generating vacuum soliton configurations in the recently popular scalar field
theories of noncommutative coordinates is also demonstrated.
