Lewenstein-Sanpera decomposition of a generic 2 ⊗ 2 density matrix by using Wootters's basis

The Lewenstein-Sanpera decomposition for a generic two-qubit density matrix is obtained by using Wootters’s basis. It is shown that the average concurrence of the decomposition is equal to the concurrence of the state. It is also shown that all the entanglement content of the state is concentrated in the Wootters’s state |x1〉 associated with the largest eigenvalue λ1 of the Hermitian matrix √√ ρρ̃ √ ρ . It is shown that a given density matrix ρ with corresponding set of positive numbers λi and Wootters’s basis can transforms under SO(4, c) into a generic 2× 2 matrix with the same set of positive numbers but with new Wootters’s basis, where the local unitary transformations correspond to SO(4, r) transformations, hence, ρ can be represented as coset space SO(4, c)/SO(4, r) together with positive numbers λi. By giving an explicit parameterization we characterize a generic orbit of group of local unitary transformations.