  Quantum discord, a kind of quantum correlation based on entropic measures, is
defined as the difference between quantum mutual information and classical
correlation in a bipartite system. Procedures are available for analytical
calculation of discord when one of the parties is a qubit with dimension two
and measurements made on it to get that one-way discord. We extend now to
systems when both parties are of larger dimension, of interest to qudit-quDit
with d, D > 2 or spin chains of spins > 1/2. While recognizing that no
universal scheme is feasible, applicable to all density matrices, nevertheless
a procedure similar to that for d=2 that works for many mixed-state density
matrices remains of interest as shown by recent such applications. We focus on
this method that uses unitary operations to describe measurements, reducing
them to a compact form so as to minimize the number of variables needed for
extremizing the classical correlation, often the most difficult part of the
discord calculation. Results are boiled down to a simple recipe for that
extremization; for some classes of density matrices, the procedure even gives
trivially the final value of the classical correlation without that
extremization. A qutrit-qutrit (d=D=3) system is discussed in detail with
specific applications to density matrices for whom other calculations involved
difficult numerics. Special attention is given to the so-called X-states and
Werner and isotropic states when the calculations become particularly simple.
An appendix discusses an independent but related question of the systematics of
X-states of arbitrary dimension. It forms a second, separate, part of this
paper, extending our previous group-theoretic considerations of systematics for
qubits now to higher d.
