We provide an explicit example of a Bell inequality with 3 settings and 2
outcomes per site for which the largest violation is not obtained by the
maximally entangled state, even if its dimension is allowed to be arbitrarily
large. This complements recent results by Junge and Palazuelos
(arXiv:1007.3042) who show, employing tools from operator space theory, that
such inequalities do exist. Our elementary example provides arguably the
simplest setting in which it can be demonstrated that even an infinite supply
of EPR pairs is not the strongest possible nonlocal resource.Comment: 9 pages; Added reference to arXiv:1012.151
