Geometric interpretation of the Clauser-Horne-Shimony-Holt inequality of nonmaximally entangled states

Abstract

We show that for pure and mixed states the problem of maximizing the correlation measure in the Clauser-Horne-Shimony-Holt inequality reduces to maximizing the perimeter of a parallelogram enclosed by an ellipse characterized by the entanglement contained in the bipartite system. Our geometrical description is valid for a nonmaximally entangled state. We also determine the corresponding optimal measurements.