The Einstein-Podolsky-Rosen state maximally violates Bell's inequalities

In their well-known argument against the completeness of quantum theory, Einstein, Podolsky, and Rosen (EPR) made use of a state that strictly correlates the positions and momenta of two particles. We prove the existence and uniqueness of the EPR state as a normalized, positive linear functional of the Weyl algebra for two degrees of freedom. We then show that the EPR state maximally violates Bell's inequalities.