A Comparison of the Concurrence and the Quantum Discord in a Two-Qubit System

The quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence are investigated with the use of concurrence C and quantum discord (QD). There is a remarkable difference between the time evolution behaviors of these two correlation measures: there is a entanglement-sudden-death phenomenon in the concurrence while there is none in QD, which is valid for all of the initial states of this system, and the interval time of the entanglement death is found to be strongly dependent on the initial states and the parameters B and Δ. With the long-time limit the steady entanglement (SC) and steady quantum discord (SQD) can be obtained. The magnitudes of SC and SQD are closely related to the parameters B and Δ, while the strength of the Dzyaloshinskii–Moriya interaction, D, has no influence. In addition, the effects of the parameters B and Δ on SC and SQD display such different and complicated features that one cannot obtain a uniform law about them, thus we give an analytical explanation of this phenomenon. Lastly, it can be noted that the value of SC is not always larger than SQD, which is strongly dependent on the parameters B and Δ.