Genuine multipartite indistinguishability and its detection via the generalized Hong-Ou-Mandel effect

The question of whether two indistinguishable particles are bosons or fermions can be answered by observing the Hong-Ou-Mandel effect on a beam splitter. However, already for three particles one can consider symmetries that are neither bosonic nor fermionic. In this work, we propose a notion of a genuine multipartite indistinguishability and describe a simple method of quantifying it experimentally.