Relative Entropy of Entanglement of One Class of Two-Qubit system

The relative entropy of entanglement of a mixed state σ for a bipartite quantum system can be defined as the minimum of the quantum relative entropy over the set of completely disentangled states. Vedral et al. Phys. Rev. A 57(1998)1619 have recently proposed a numerical method to get the relative entropy of entanglement E_re for two-qubit systems. This paper shows that the convex programming method can be applied to calculate E_re of two-qubit systems analytically, and discusses the conditions under which the method can be adopted.