  We present an analytical solution for classical correlation, defined in terms
of linear entropy, in an arbitrary $d\otimes 2$ system when the second
subsystem is measured. We show that the optimal measurements used in the
maximization of the classical correlation in terms of linear entropy, when used
to calculate the quantum discord in terms of von Neumann entropy, result in a
tight upper bound for arbitrary $d\otimes 2$ systems. This bound agrees with
all known analytical results about quantum discord in terms of von Neumann
entropy and, when comparing it with the numerical results for $10^6$ two-qubit
random density matrices, we obtain an average deviation of order $10^{-4}$.
Furthermore, our results give a way to calculate the quantum discord for
arbitrary $n$-qubit GHZ and W states evolving under the action of the amplitude
damping noisy channel.
