  Ionicioiu and Spiller [Phys. Rev. A 85, 062313 (2012)] have recently
presented an axiomatic framework for mapping graphs to quantum states of a
suitable physical system. Based on their study, we first extend the axiomatic
framework to hypergraphs by means of modifying its axioms and consistency
conditions. Then we use the axiomatic approach to encode hypergraphs into a new
family of quantum states, called the hypergraph states. Moreover, we also try
to do the followings: (i) to show that real equally weighted states, which
occur in Grover and Deutsch-Joza algorithms, are equivalent to hypergraph
states; (ii) to describe the relations among hypergraph states, graph states
and stabilizer states; (iii) to provide some transformation rules, stated in
purely hypergraph theoretical terms, which completely characterize the
evolution of hypergraph states under some local operations, including operators
in Pauli group and some special local Pauli measurements; and (iv) to
investigate some properties of multipartite entanglement of hypergraph states
by hypergraph theory.
