Analytical solutions and criteria for the quantum discord of two-qubit X-states

Except for a few special states, computing quantum discord remains a complicated optimization process. In this paper we present analytical solutions for computing quantum discord of the most general class of X-states and the criteria for each analytical solution to be valid. We discuss parameter regions that correspond to different analytical solutions and explain the underlying reasons for such structure to exist. We apply our formalism to study both arbitrary X-states and X-states with certain symmetries. We find that our analytical formalism is in excellent agreement with numerical calculation of quantum discord in both cases.