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.

• Received 4 November 2004

DOI:https://doi.org/10.1103/PhysRevA.71.032107