  We study the separability of bipartite quantum systems in arbitrary
dimensions using the Bloch representation of their density matrix. This
approach enables us to find an alternative characterization of the separability
problem, from which we derive a necessary condition and sufficient conditions
for separability. For a certain class of states the necessary condition and a
sufficient condition turn out to be equivalent, therefore yielding a necessary
and sufficient condition. The proofs of the sufficient conditions are
constructive, thus providing decompositions in pure product states for the
states that satisfy them. We provide examples that show the ability of these
conditions to detect entanglement. In particular, the necessary condition is
proved to be strong enough to detect bound entangled states.
