Ri Qu, Juan Wang, Zong-shang Li, Yan-ru Bao
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. We generalize the axiomatic framework to encode hypergraphs into quantum states. We define a new family of quantum states of n qubits, called by the hypergraph states, by using the axiomatic approach. We show that real equally weighted states which occur in some quantum algorithms, including Grover search algorithm, Deutsch-Joza algorithm, etc., are equivalent to hypergraph states. We describe the relations among hypergraph states, graph states and stabilizer states. We translate the action of some local operations, including operators in Pauli group and some special local Pauli measurements, on hypergraph states into the transforms on their corresponding hypergraphs. Moreover, we also investigate some properties of multipartite entanglement of hypergraph states.
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http://arxiv.org/abs/1211.3911
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