Special entangled quantum systems and the Freudenthal construction

Abstract

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