  We present a general strategy to derive entanglement criteria which consists
in performing a mapping from qudits to qubits that preserves the separability
of the parties and SU(2) rotational invariance. Consequently, it is possible to
apply the well known positive partial transpose criterion to reveal the
existence of quantum correlations between qudits. We discuss some examples of
entangled states that are detected using the proposed strategy. Finally, we
demonstrate, using our scheme, how some variance-based entanglement witnesses
can be generalized from qubits to higher dimensional spin systems.
