Abstract
We relate the nonlocal properties of noisy entangled states to Grothendieck’s constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states , we show that there is a local model for projective measurements if and only if , where is Grothendieck’s constant of order 3. Known bounds on prove the existence of this model at least for , quite close to the current region of Bell violation, . We generalize this result to arbitrary quantum states.
- Received 23 November 2005
DOI:https://doi.org/10.1103/PhysRevA.73.062105
©2006 American Physical Society