  We consider special quantum systems containing both distinguishable and
identical constituents. It is shown that for these systems the Freudenthal
construction based on cubic Jordan algebras naturally defines entanglement
measures invariant under the group of stochastic local operations and classical
communication (SLOCC). For this type of multipartite entanglement the SLOCC
classes can be explicitly given. These results enable further explicit
constructions of multiqubit entanglement measures for distinguishable
constituents by embedding them into identical fermionic ones. We also prove
that the Plucker relations for the embedding system provide a sufficient and
necessary condition for the separability of the embedded one. We argue that
this embedding procedure can be regarded as a convenient representation for
quantum systems of particles which are really indistinguishable but for some
reason they are not in the same state of some inner degree of freedom.
