  We consider the action of the group of local unitary transformations, U(m) x
U(n), on the set of (mixed) states W of the bipartite m x n quantum system. We
prove that the generic U(m) x U(n)--orbits in W have dimension m^2+n^2-2. This
problem was mentioned (and left open) by Kus and Zyczkowski in their paper
Geometry of entangled states. The proof can be extended to the case of
arbitrary finite-dimensional multipartite quantum systems.
