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Several families of states such as Werner states, Bell-diagonal states, and Dicke states are useful in understanding multipartite entanglement. Here we present a (2N+1-1)-parameter family of N-qubit "X states" that embraces all those families, generalizing previously defined states for two qubits. We also present the algebra of the operators that characterize the states and an iterative construction for this algebra, a subalgebra of su(2N). We show how a variety of entanglement witnesses can detect entanglement in such states. Connections are also made to structures in projective geometry. © 2010 The American Physical Society.

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Physical Review A - Atomic, Molecular, and Optical Physics