We evaluate analytically the quantum discord for a large family of multiqubit states. It is interesting to note that the quantum discord of three-qubits and five-qubits is the same, as is the quantum discord of two-qubits and six-qubits. We discover that the quantum discord of this family states can be concluded into three categories. The level surfaces of the quantum discord in the three categories is shown through images. Furthermore, we investigated the dynamic behavior of quantum discord under decoherence. For the odd partite systems, we prove the frozen phenomenon of quantum discord doesn't exist under the phase flip channel, while it can be found in the even partite systems.

9 pages, 2 figures, comments are welcome!. arXiv admin note: text overlap with arXiv:2104.12344