Multipartite entanglement in 2 x 2 x n quantum systems

Abstract

We classify multipartite entangled states in the Hilbert space H=C-2 x C-2 x C-n (ngreater than or equal to4), for example, the four-qubit system distributed over three parties, under local filtering operations. We show that there exist nine essentially different classes of states, giving rise to a five-graded partially ordered structure, including the celebrated Greenberger-Home-Zeilinger and W classes of three qubits. In particular, all 2 X 2 X n states can be deterministically prepared from one maximally entangled state, and some applications such as entanglement swapping are discussed