Relative entropy of entanglement of two-qubit 'X' states

Two closest single-qubit states could be diagonalised by the same unitary matrix, which helps to find the relative entropy of entanglement of a two-qubit 'X' state. We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit 'X' state. This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states, such as pure states, Werner states, and so on.