Lluis Masanes, Markus P. Mueller, David Perez-Garcia, Remigiusz Augusiak
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 the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories interacting dynamics is impossible. Within the formalism of generalized probability theory entanglement seems to be a generic feature, but our results suggest that, once dynamics is taken into account, entanglement is a very singular phenomenon.
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http://arxiv.org/abs/1111.4060
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