Physics – Mathematical Physics
Scientific paper
2010-12-03
J. Phys. A: Math. Theor. 44 (2011) 175302 (21pp)
Physics
Mathematical Physics
23 pages, minor corrections, the final version to appear in J. Phys. A.: Math. Theor
Scientific paper
10.1088/1751-8113/44/17/175302
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. In addition, for Bose and Fermi statistics, we construct an analog of the Jamiolkowski isomorphism.
Grabowski Janusz
Kus Marek
Marmo Giuseppe
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