Efficient generation of a maximally entangled state by repeated on- and off-resonant scattering of ancilla qubits

A scheme for preparing two fixed noninteracting qubits in a maximally entangled state is presented. By repeating on- and off-resonant scattering of ancilla qubits, the target qubits are driven from an arbitrary initial state into a 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.