All non-locally Realized Continuous Variable Bipartite Gaussian States are Entangled

We investigate the connection between entanglement and non-locality between continuous-variable bipartite Gaussian states. The investigation initiates with formulating non-locality by using the phase-space Wigner representation of Bell’s function. Furthermore, our analysis shows entanglement to be necessary for nonlocality, but not sufficient for it; however, nonlocality is sufficient to ensure entanglement.