Maximal Violation of Bell’s Inequalities for Continuous Variable Systems

We generalize Bell’s inequalities to biparty systems with continuous quantum variables. This is achieved by introducing the Bell operator in perfect analogy to the usual spin- $1/2$ systems. It is then demonstrated that two-mode squeezed vacuum states display quantum nonlocality by using the generalized Bell operator. In particular, the original Einstein-Podolsky-Rosen states, which are the limiting case of the two-mode squeezed vacuum states, can maximally violate Bell’s inequality due to Clauser, Horne, Shimony, and Holt. The experimental aspect of our scheme is briefly considered.