Entanglement and the three-dimensionality of the Bloch ball
arXiv:1111.4060
Abstract
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. This result reveals that "existence of entanglement" is the requirement with minimal logical content which singles out quantum theory from our family of theories.
30 pages + appendix, 2 figures
References in corpus (7)
- Informational derivation of Quantum Theory
- Existence of an information unit as a postulate of quantum theory
- Reformulating and Reconstructing Quantum Theory
- Deriving quantum theory from its local structure and reversibility
- If no information gain implies no disturbance, then any discrete physical theory is classical
- How uncertainty enables non-classical dynamics
- Information processing in convex operational theories