  Unlike for bipartite states consisting of distinguishable particles, in the
case of identical parties the notion of entanglement is still under debate. In
the following, we review two different approaches to the entanglement of
systems consisting of two Bosons or Fermions; the first approach is based on
the particle aspect typical of first quantization and identifies separable pure
states as those that allow to assign two orthogonal single particle vector
states to both parties. The second approach makes full use of the mode aspect
of second quantization whereby separability can be formulated as absence of
non-local correlation among two different sets of modes. While the first
approach applies to pure states only, the second one is more general and
characterizes generic entangled states. In the following, we shall show that
the mode-based approach indeed contains the particle-based one.
