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Gouy phase in non-classical paths in triple-slit interference experiment

We propose a simple model to study the Gouy phase effect in the triple-slit experiment in which we consider a non-classical path. The Gouy phase differs for classical or non-classical paths as it depends on the propagation time. In this case the Gouy phase difference changes the Sorkin parameter $κ$ used to estimate non-classical path contribution in a nontrivial way shedding some light in the implementation of experiments to detect non-classical path contributions.