  We describe a generic way to improve a given linear entanglement witness by a
quadratic, nonlinear term. This method can be iterated, leading to a whole
sequence of nonlinear witnesses, which become stronger in each step of the
iteration. We show how to optimize this iteration with respect to a given
state, and prove that in the limit of the iteration the nonlinear witness
detects all states that can be detected by the positive map corresponding to
the original linear witness.
