Maximal violation of tight Bell inequalities for maximal high-dimensional entanglement

We propose a Bell inequality for high-dimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even d-dimensional measurement outcomes for which this Bell inequality is maximally violated by maximally entangled states. Furthermore, we demonstrate that the Bell inequality is applicable to continuous variable systems and yields strong violations for two-mode squeezed states.