Qudit hypergraph states and their properties

Hypergraph states, a generalization of graph states, constitute a large class of quantum states with intriguing nonlocal properties, and they have promising applications in quantum information science and technology. In this paper, we study some features of an independently proposed generalization of hypergraph states to qudit hypergraph states, i.e., each vertex in the generalized hypergraph (multi-hypergraph) represents a d-level system instead of a two-level one. It is shown that multi-hypergraphs and d-level hypergraph states have a one-to-one correspondence, and the structure of a multi-hypergraph exhibits the entanglement property of the corresponding quantum state. We discuss their relationship with some well-known state classes, e.g., real equally weighted states and stabilizer states. The Bell nonlocality, an important resource in fulfilling many quantum information tasks, is also investigated.