  We present the modified relative entropy of entanglement for multi-party
systems by a given relative density matrix which is spanned by a linear
combination of the direct products of so-called basis of relative density
matrices and reduced density matrices for every party. For three qubit system
in a pure state we derive out the explicit and closed expression of our
relative density matrix which is a function of the components of the state
vector of three qubits. Through computing the modified relative entropy of
entanglement of some important and interesting examples, we display the main
behaviors and elementary properties of the modified relative entropy of
entanglement and compare it with the generalized entanglement of formation.
Moreover, we also propose an assistant, as the upper bound, of the modified
relative entropy of entanglement.
