Quantum Discord for Three-qubit Extended X-states

In this paper, we investigate the quantum discord for a family of three-qubit extended X-states and give analytic formulas of the quantum discord for three-qubit states in several cases, including two zero quantum discord cases and the Werner-GHZ state case. Moreover, we inspect the dynamic behavior of the quantum discord for the three-qubit states under the phase damping channel. It is shown that the frozen phenomenon of quantum discord exists for some states under phase damping channel, while it does not exist for some other states. In particular, the quantum discord of the Werner-GHZ state monotonically decreases to zero under the phase damping channel.