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

Special entangled quantum systems and the Freudenthal construction