Detection statistics in a double-double-slit experiment

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 they can be detected in completely different timescales. As the detection of the first particle leads to collapse of the wave function, there is no a straightforward and agreed-upon method to study this problem in the orthodox formalism which lacks a clear prediction of these random events and therefore the quantum state afterward. This is not the case in the 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 that 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 conditions.

Automated summary

In this paper, the statistics of detection data in a general double-double-slit experiment are analyzed. The detection times of the two particles are generally unequal, and the distances of left and right screens from their slits, as well as the ratio, have no constraints, leading to different timescales of detection. While the orthodox formalism lacks a clear prediction of random events and the quantum state afterward, the Bohmian framework implemented in this paper provides a straightforward method to study this problem and predict the system up to the end of the experiment. The main result is the joint distribution of detection data, including the arrival time and position of particles on left and right screens. It is observed that while the joint spatial distribution can be affected by changes to the relative location of screens, the marginals on each side remain intact, supporting signal locality. Furthermore, the result is shown to be highly sensitive to quantum equilibrium conditions.