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Hypergraph states form a family of multiparticle quantum states thatgeneralizes cluster states and graph states. We study the action and graphicalrepresentation of nonlocal unitary transformations between hypergraph states.This leads to a generalization of local complementation and graphical rules forvarious gates, such as the CNOT gate and the Toffoli gate. As an application,we show that already for five qubits local Pauli operations are not sufficientto check local equivalence of hypergraph states. Furthermore, we use our rulesto construct entanglement witnesses for three-uniform hypergraph states.

Graphical description of unitary transformations on hypergraph states