Maximal Bell's inequality violation for non-maximal entanglement

Bell's inequality violation (BIQV) for correlations of polarization is studied for a product state of two two-mode squeezed vacuum (TMSV) states. The violation allowed is shown to attain its maximal limit for all values of the squeezing parameter, ζ. We show via an explicit example that a state whose entanglement is not maximal allow maximal BIQV. The Wigner function of the state is non-negative and the average value of either polarization is nil