Entanglement of formation from optimal decomposition

We present a new method of analytically deriving the entanglement of formation of the bipartite mixed state. The method realizes the optimal decomposition families of states. Our method can lead to many new results concerning entanglement of formation, its additivity and entanglement cost. We illustrate it by investigating the two-qubit state, the separable state, the maximally correlated state, the isotropic state and the Werner state.