  We analyze the optimal measurements accessing classical correlations in
arbitrary two-qubit states. Two-qubit states can be transformed into the
canonical forms via local unitary operations. For the canonical forms, we
investigate the probability distribution of the optimal measurements. The
probability distribution of the optimal measurement is found to be centralized
in the vicinity of a specific von Neumann measurement, which we call the
maximal-correlation-direction measurement (MCDM). We prove that for the states
with zero-discord and maximally mixed marginals, the MCDM is the very optimal
measurement. Furthermore, we give an upper bound of quantum discord based on
the MCDM, and investigate its performance for approximating the quantum
discord.
