Reviewing pigeonhole effect with transversal modes

Abstract

We investigate the interference setup claimed to reveal the quantum pigeonhole effect. It is a claim that it is possible that three parties travel across a two-path interferometer, but no pair of them share a path. We demonstrate the inconsistency of the description based on the weak values. We introduce transversal modes and observe the arise of correlations between path and traversal degrees of freedom. Also, the rotational symmetry of the output pattern is studied as a witness of pairwise interaction. It shows no apparent relation to the probability of observing three particles in the same output.