QUROPE Quantum Information Processing and Communication in Europe

We explore the existence of entangling dynamics in a large family of theories which contains quantum theory as a special case. We classify all continuously-reversible and locally-tomographic theories for bipartite systems where each subsystem has a state space with the geometry of a Euclidean ball (like the Bloch ball of a qubit but with dimension not necessarily equal to three). We show that the only theory in this family which has interacting dynamics is quantum theory, and all the other theories do not allow for entanglement nor violation of Bell inequalities. This suggests that, once dynamics is taken into account, entanglement and violation of Bell inequalities are very singular phenomena.