On detection statistics in double-double-slit experiment

Abstract: In this paper, we analyze the statistics of detection data in a general double-double-slit experiment. The two particles are detected at random times which are not equal in general and because we do not have any constraint on the distances of left and right screens from their slits and the ratio as well, they can be detected in completely different timescales. As the detection of first particle leads to collapse of the wave function, there is no a straightforward and agreed method to study this problem in the orthodox formalism which lacks a clear prediction of these random events and therefore the quantum state afterwards. This is not the case in Bohmian framework which we implement in this paper and we can predict the system up to the end of experiment. The main result is the joint distribution of detection data including the arrival time and position of the particles on left and right screens. As one of the main consequences, we see, although the joint spatial distribution can be affected by a change to the relative location of screens, the marginals on each side remain intact compatible with signal-locality. At the end, we see how this result is very sensitive to quantum equilibrium condition.