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arXiv:1111.4812 · Journal of Physics A Mathematical and Theoretical

Segre maps and entanglement for multipartite systems of indistinguishable particles

Janusz Grabowski, Marek Kuś, Giuseppe Marmo

Published Feb 21, 2012• 11 citations
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Abstract

We elaborate the concept of entanglement for multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics. The entanglement is characterized in terms of generalized Segre maps, supplementing thus an algebraic approach to the problem by a more geometric point of view.
DOI
10.1088/1751-8113/45/10/105301

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We analyze the concept of entanglement for a 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 an 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 Jamiołkowski isomorphism.
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