  This work is an enquiry into the circumstances under which entropy methods
can give an answer to the questions of both quantum separability and classical
correlations of a composite state. Several entropy functionals are employed to
examine the entanglement and correlation properties guided by the corresponding
calculations of concurrence. It is shown that the entropy difference between
that of the composite and its marginal density matrices may be of arbitrary
sign except under special circumstances when conditional probability can be
defined appropriately. This ambiguity is a consequence of the fact that the
overlap matrix elements of the eigenstates of the composite density matrix with
those of its marginal density matrices also play important roles in the
definitions of probabilities and the associated entropies, along with their
respective eigenvalues. The general results are illustrated using pure and
mixed state density matrices of two-qubit systems. Two classes of density
matrices are found for which the conditional probability can defined: (1)
density matrices with commuting decompositions and (2) those which are
decohered in the representation where the density matrices of the marginals are
diagonal. The first class of states encompass those whose separability is
currently understood as due to particular symmetries of the states. The second
are a new class of states which are expected to be useful for understanding
separability. Examples of entropy functionals of these decohered states
including the crucial isospectral case are discussed.

Quantum Physics