Quantum nonlocality and quantum key distribution with the two-mode Gaussian equally squeezed state of continuous-variable systems

We propose a scheme for generating the two-mode Gaussian equally squeezed state (GESS) by using the optical method and analyze the entanglement properties of this state by means of the logarithmic negativity. It is shown that such a two-mode GESS contains the same amount of entanglement as the two-mode squeezed vacuum state (TSVS). We investigate quantum nonlocality for this state by using two-mode Wigner function measurement. It is found that the operations of local squeezing and distancing can effectively enhance the degree of quantum nonlocality. We propose a quantum key distribution scheme based on the two-mode GESS, and we show that the proposed scheme is more secure against the partial interception attack strategy than one with Einstein-Podolsky-Rosen (EPR) pairs even though the transmission coefficient of the eavesdropping beam splitter is rather low.