We construct quantum gates entanglers for different classes of multipartite states. In particular, we construct entangler operators for W and GHZ classes of multipartite states based on the construction of the concurrence classes. We also discuss in detail these two classes of the quantum gates entanglers for three-partite states.
We construct quantum gate entanglers for different classes of multipartite states based on definition of W and GHZ concurrence classes. First, we review the basic construction of concurrence classes based on orthogonal complement of a positive operator valued measure (POVM) on quantum phase. Then, we construct quantum gates entanglers for different classes of multi-qubit states. In particular, we show that these operators can entangle multipartite state if they satisfy some conditions for W and GHZ classes of states. Finally, we explicitly give the W class and GHZ classes of quantum gate entanglers for four-qubit states.
We propose two classes of the generalized concurrence vectors of the multipartite systems consisting of qubits. Making use of them, we are able to, respectively, describe and quantify GHZ-class and W-class entanglement both in total and between arbitrary two partite in the multipartite system consisting of qubits. In the case of pure state of three qubits that one partite is separable, it is shown to exactly back to the usual Wootters' concurrence after introduce a whole concurrence vector. In principle, our method is applicable to any N-partite systems consisting of N qubits.