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The hypergraph states are pure multipartite quantum states corresponding to ahypergraph. It is an equal superposition of the states belonging to thecomputational basis. Given any hypergraph, we can construct a hypergraph statedetermined by a Boolean function. In contrast, we can find a hypergraph,corresponding to a Boolean function. This investigation develops a number ofcombinatorial structures concerned with the hypergraph states. For instance,the elements of the computational basis generate a lattice. The chains andantichains in this lattice assist us to find the equation of the Booleanfunction explicitly as well as to find a hypergraph. In addition, weinvestigate the entanglement property of the hypergraph states in terms oftheir combinatorial structures. We demonstrate several classes of hypergraphs,such that every cut of equal length on the corresponding hypergraph states hasan equal amount of entanglement.

A Boolean Functions Theoretic Approach to Quantum Hypergraph States and Entanglement