  The elements of reality coined by Einstein, Podoslky, and Rosen promoted a
series of fundamental discussions involving the notion of quantum correlations
and physical realism. The superposition principle applied in the double-slit
experiment with matter waves highlights the need for a critical review of the
adoption of physical realism in the quantum realm. In this work, we employ a
measure of physical irrealism and consider an initial contractive state in the
double-slit setup for which position and momentum variables of a single
particle are initially correlated. We investigate how the behavior of the
irrealism can help us to obtain information about the interference pattern,
wavelike, and particle-like properties in the double-slit setup with matter
waves. We find that there is a time of propagation that minimizes the
irrealism, and around this point the state at the detection screen is squeezed
in position and momentum in comparison with the standard Gaussian
superposition. Interestingly, we show that the maximum visibility and the
number of interference fringes are related to the minimum of the irrealism.
Moreover, we demonstrate a monotonic relation between the irrealism and
visibility around the time of minimum. Then, we argue how to use these results
to indirectly measure the irrealism for position variable from the fringe
visibility.
