Classification of multipartite entanglement of all finite dimensionality.

  title={Classification of multipartite entanglement of all finite dimensionality.},
  author={Gilad Gour and Nolan Wallach},
  journal={Physical review letters},
  volume={111 6},
We provide a systematic classification of multiparticle entanglement in terms of equivalence classes of states under stochastic local operations and classical communication (SLOCC). We show that such a SLOCC equivalency class of states is characterized by ratios of homogenous polynomials that are invariant under local action of the special linear group. We then construct the complete set of all such SL-invariant polynomials (SLIPs). Our construction is based on Schur-Weyl duality and applies to… 

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