Multicomponent correlation functions are developed by utilizing
d-outcome measurements. Based on multicomponent correlation functions, we propose a Bell inequality for bipartite
d-dimensional systems. Violation of the Bell inequality for continuous-variable (CV) systems is investigated. The violation of maximally entangled states can exceed the Cirel'son bound; the maximal violation is 2.969 81. For finite values of the squeezing parameter, the violation strength of CV states increases with dimension
d. Numerical results show that the violation strength of CV states with finite squeezing parameters is stronger than that of maximally entangled states.
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.
A Bell inequality is a fundamental test to rule out local hidden variable model descriptions of correlations between two physically separated systems. There have been a number of experiments in which a Bell inequality has been violated using discrete-variable systems. We demonstrate a violation of Bell's inequality using continuous variable quadrature measurements. By creating a four-mode entangled state with homodyne detection, we recorded a clear violation with a Bell value of B=2.31±0.02. This opens new possibilities for using continuous variable states for device independent quantum protocols.