Four-qubit entangled symmetric states with positive partial transpositions

@article{Brugus2012FourqubitES,
  title={Four-qubit entangled symmetric states with positive partial transpositions},
  author={Jordi Tura i Brugu{\'e}s and Remigiusz Augusiak and Philipp Hyllus and Marek Ku's and Jan Samsonowicz and Maciej Lewenstein},
  journal={Physical Review A},
  year={2012},
  volume={85},
  pages={060302}
}
We solve the open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical method that allows to construct multipartite PPT entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states. Second, we adapt the algorithm allowing to search for extremal elements in the convex set of bipartite PPT states [J. M. Leinaas, J… 

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