Multicomponent Bell inequality and its violation for continuous-variable systems

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 sCVd 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.