Entanglement for multipartite systems of indistinguishable particles

Résumé : We analyze the concept of entanglement for multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics. We use the representation theory of symmetry groups to formulate a unified approach to this problem in terms of simple tensors with appropriate symmetry. For an arbitrary parastatistics, we define the S-rank generalizing the notion of the Schmidt rank. The S-rank, defined for all types of tensors, serves for distinguishing entanglement of pure states. We characterize the entanglement also in terms of generalized Segre maps. In addition, for Bose and Fermi statistics, we construct an analog of the Jamiolkowski isomorphism.