  Selection of an ensemble of equally prepared quantum systems, based on
measurements on it, is a basic step in quantum state purification. For an
ensemble of single qubits, iterative application of selective dynamics has been
shown to lead to complex chaos, which is a novel form of quantum chaos with
true sensitivity to the initial conditions. The Julia set of initial valuse
with no convergence shows a complicated structre on the complex plane. The
shape of the Julia set varies with the parameter of the dynamics. We present
here results for the two qubit case demonstrating how a purification process
can be destroyed with chaotic oscillations.
