  A scheme for preparing two fixed non-interacting qubits in a maximally
entangled state is presented. By repeating on- and off-resonant scattering of
ancilla qubits, the state of the target qubits is driven from an arbitrary
initial state into the singlet state with probability 1 (perfect efficiency).
Neither the preparation nor the post-selection of the ancilla spin state is
required. The convergence from an arbitrary input state to the unique fixed
point (mixing property) is proved rigorously, and its robustness is
investigated, by scrutinizing the effects of imperfections in the incident wave
of the ancilla, such as mistuning to a resonant momentum, imperfect
monochromatization, and fluctuation of the incident momentum, as well as
detector efficiency.
