Quantifying quantum discord and entanglement of formation via unified purifications

We propose a scheme to evaluate the amount of quantum discord and entanglement of formation for mixed states and reveal their ordering relation via an intrinsic relationship between the two quantities distributed in the purification of different states. This approach enables us to achieve analytical expressions of the two measures for some quantum states, such as an arbitrary two-qubit density matrix reduced from pure three-qubit states and a class of rank-2 mixed states of 4 x 2 systems. Moreover, we apply the scheme to characterize fully the dynamic behavior of quantum correlations for the specified physical systems under decoherence.