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- Limits on non-local correlations from the structure of the local state space

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10120032

Nonlocality is arguably one of the most remarkable features of

quantum mechanics. On the other hand nature seems to forbid other

no-signaling correlations that cannot be generated by quantum systems.

Usual approaches to explain this limitation is based on information

theoretic properties of the correlations without any reference to

physical theories they might emerge from. However, as shown in [PRL 104,

140401 (2010)], it is the structure of local quantum systems that

determines the bipartite correlations possible in quantum mechanics. We

investigate this connection further by introducing toy systems with

regular polygons as local state spaces. This allows us to study the

transition between bipartite classical, no-signaling and quantum

correlations by modifying only the local state space. It turns out that

the strength of nonlocality of the maximally entangled state depends

crucially on a simple geometric property of the local state space, known

as strong self-duality. We prove that the limitation of nonlocal

correlations is a general result valid for the maximally entangled state

in any model with strongly self-dual local state spaces, since such

correlations must satisfy the principle of macroscopic locality. This

implies notably that TsirelsonÃ¢ÂÂs bound for correlations of the maximally

entangled state in quantum mechanics can be regarded as a consequence of

strong self-duality of local quantum systems. Finally, our results also

show that there exist models which are locally almost identical to

quantum mechanics, but can nevertheless generate maximally nonlocal

correlations.

©2012 Perimeter Institute for Theoretical Physics