Quantum multigraph states and multihypergraph states

In this paper we propose two classes of multiparticle entangled states: multigraph and multihypergraph states. Two types of operations are designed to correspond to the edges and hyperedges to prepare the states. Furthermore, multigraph and multihypergraph states contain qudit graph and hypergraph states, respectively. More interestingly, we demonstrate the one-to-one correspondence between the proposed multihypergraph states and the generalized real equally weighted states when the dimension of the states is an odd prime.