Modification of relative entropy of Entanglement

We present the modified relative entropy of entanglement (MRE) in order to both improve the computability for the relative entropy of entanglement and avoid the problem that the entanglement of formation seems to be greater than entanglement of distillation. For two qubit system we derive out an explicit and "weak" closed expression of MRE that depends on the pure state decompositions in the case of mixed states. For more qubit system, we obtain an algorithm to calculate MRE in principle. MRE significantly improves the computability of relative entropy of entanglement and decreases the dependence and sensitivity on the pure state decompositions. Moreover it is able to inherit most of the important physical features of the relative entropy of entanglement. In addition, a kind of states, as an extension of Werner's states, is discussed constructively.