M. Rossi, M. Huber, D. Bruß, C. Macchiavello
We introduce a class of multiqubit quantum states which generalizes graph states. These states are derived from an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. As for graph states, a generalised stabilizer formalism is derived to describe this class of states. We study how these states can be classified in entanglement inequivalent classes by means of $k$-uniformity. Finally we disclose a one-to-one correspondence with states employed in quantum algorithms, such as Deutsch-Jozsa's and Grover's.
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http://arxiv.org/abs/1211.5554
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