  In this paper, we compute a recursive wall-crossing formula for the
Poincar\'e polynomials and Euler characteristics of Abelian symplectic
quotients of a complex projective manifold under a special effective action of
a torus with non-trivial characters. An analogy can be made with the space of
pure states of a composite quantum system containing $r$ quantum bits under
action of the maximal torus of Local Unitary operations.
