Entanglement and the three-dimensionality of the Bloch ball

@article{Masanes2011EntanglementAT,
  title={Entanglement and the three-dimensionality of the Bloch ball},
  author={Lluis Masanes and Markus P. Mueller and David P{\'e}rez-Garc{\'i}a and Remigiusz Augusiak},
  journal={Journal of Mathematical Physics},
  year={2011},
  volume={55},
  pages={122203}
}
We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state space. In addition to this, we impose two very natural assumptions: the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for… 

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