Nonlocality of two- and three-mode continuous variable systems

We address the nonlocality of fully inseparable three-mode Gaussian states generated either by bilinear three-mode Hamiltonians or by a sequence of bilinear two-mode Hamiltonians. Two different tests revealing nonlocality are considered, in which thedichotomic Bell operator is represented by the displaced parity andbythe pseudospin operator respectively. Three-mode states arealso considered as a conditional source of two-mode non-Gaussian states,whose nonlocality properties are analysed. We found that the non-Gaussian character of the conditional states allows violation of Bell’s inequalities (by parity and pseudospin tests) stronger than with a conventional twin-beam state. However, the non-Gaussian character is not sufficienttoreveal nonlocality through a dichotomized quadrature measurement strategy.