Bell’s inequality for an entanglement of nonorthogonal states

Given an entanglement of two systems involving nonorthogonal states, we find the Schmidt decomposition for the state. The relation between the Schmidt representation and an ideal measurement of the degree of entanglement of the states is discussed, and a Bell inequality is shown to be violated. The maximal violation of the Bell inequality provides a measurement of the degree of entanglement. The entangled coherent states are provided as a concrete example of the Bell inequality for entangled nonorthogonal states.