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.
In this paper, we will define concurrence classes for a general multipartite state based on an orthogonal complement of a positive operator valued measure on quantum phase. In particular, we will define concurrence for an arbitrary bipartite state and concurrence classes for the three- and four-partite states. And finally, we will define concurrence for
Wm and
GHZm classes of a general multipartite state.