Abstract
In this paper, we investigate the convergence behavior of the fixed-point search algorithm with two arbitrary equal phase shifts for any number of iterations. We show that no matter what the initial deviation is, the algorithm converges to the target state with certainty for phase shifts between 0 and π∕2, and to the target state with the success probabilities of at least 80% and at least 66% for phase shifts between π∕2 and arccos(-1/4) and between arccos(-1/4) and 2π/3, respectively, while the algorithm does not converge for phase shifts between 2π/3 and π.
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