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Abstract
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We present su±cient criteria for the entanglement of three-qubit states. For some special
families of states, the criteria are also necessary for the entanglement. They are formulated
as simple sets of inequalities for the mean values of certain observables de¯ned as tensor
products of Pauli matrices. The criteria are good indicators of the entanglement in the vicinity of
three-qubit GHZ and W states and enjoy the capability of detecting the entangled states with
positive partial transpositions. Furthermore, they improve the best known result for the case of
W state mixed with the white noise. The e±ciency of the criteria is illustrated through several
examples.
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