Multipartite entanglement classes of a multiport beam splitter

The states generated by a multiport beam splitter usually display genuine multipartite entanglement between the many spatial modes. Here we investigate the different classes of multipartite entangled states that arise in this practical situation, working within the paradigm of stochastic local operations with classical communication. We highlight three scenarios, one where the multipartite entanglement classes follow a total number hierarchy, another where the various classes follow a nonclassicality degree hierarchy, and a third one that is a combination of the previous two. Moreover, the multipartite entanglement of higher-dimensional versions of Dicke states relates naturally to our results.