Effects of detector size and position on a test of Born's rule using a three-slit experiment

Recent high-precision measurements in a three-slit diffraction experiment [Sinha et al., Science 329, 418 (2010)] have been performed as an explicit test of the validity of Born's rule for quantum probabilities. This experiment aims to establish an upper limit to the possibility of higher-order interference, which, if observed, could support generalization of quantum probability theory. We reproduce this three-slit experiment using position-resolved detection, compare our results to a computational model, and find significant limitations to the normalization scheme proposed by Sinha et al. that influence interpretation. We further show that the dependence of the measurements on detector size and position must be taken into account for proper interpretation of results and meaningful comparison with other experimental schemes.

Figure 1

Experimental setup. The different combinations of open and closed slits are achieved by adjusting the position of the mask with respect to the stationary three slits. Dimensions of the slits and mask apertures are shown at right. (Bottom) Typical diffraction pattern corresponding to all three slits open [$p_{ABC}\left(\mathbf{r}\right)$].

Figure 2

Measured (a–c) and simulated (d–f) $\epsilon$, $\delta$, and $\kappa$ as a function of detector size. The gray-shaded region indicates one standard deviation above the mean. Dashed lines indicate $\delta$ calculated in the absence of any error.

Figure 3

Calculated $\delta$ as a function of both position and detector size, given (a) our experimental parameters and (b) Sinha et al.'s experimental parameters, with no simulated experimental error.

Figure 4

Simulated $\epsilon$, $\delta$, and $\kappa$ as a function of detector size (a–c) and position (d–f), given the experimental parameters and systematic error in the mask described in [6]. Plots (g–i) show how reducing the size of the detector from 62.5 to 7 $\mu$m changes these parameters. The gray-shaded region indicates one standard deviation above the mean. Dashed lines indicate $\delta$ calculated in the absence of any error.

Figure 5

Measured (a–c) and simulated (d–f) $\epsilon$, $\delta$, and $\kappa$ as a function of position. The gray-shaded region indicates one standard deviation above the mean.