Fair sampling perspective on an apparent violation of duality

In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that "the simultaneous observation of wave and particle behavior is prohibited" [Scully MO, Englert B-G, Walther H (1991) Nature 351:111-116]. Whereas wave behavior is associated with the observation of interference fringes, particle behavior generally corresponds to the acquisition of which-path information by means of coupling the paths to a measuring device or part of their environment. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, postselected measurements on specific degrees of freedom of the environment of the two-path state. Our work gives insight into a possible mechanism for obtaining simultaneous high which-path information and high-visibility fringes in a single experiment. Further, our results introduce previously unidentified avenues for experimental tests of duality.