Fringe visibility, which-way information and weak value

We show how to obtain both complete which-way information and a perfect interference pattern simultaneously in a double-slit experiment using a quantum weak value scheme. It does not violate the wave-particle duality since we select only part of the interference data based on the post-selection of the final state following the idea of a weak value. We also show that our scheme is robust in consideration of generalized set-ups using spin models.