Quantum Discord of Non-X State

The level surfaces of quantum discord for a class of two-qubit states are investigated when the Bloch vectors and are perpendicularly oriented. The geometric objects of tetrahedron T and octahedron O are deformed. The level surfaces of constant discord are formed by three interaction "tubes" along three orthogonal directions. They shrink to the center when the Bloch vectors are increased and are expanded and cut off by the state tetrahedron T when the quantum discord is increased. In the phase damping channel, the quantum discord keeps approximately a constant when the time increases.