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

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