# 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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