Bell inequalities for continuous-variable systems in generic squeezed states

Bell inequalities for continuous-variable bipartite systems are studied. The inequalities are expressed in terms of pseudo-spin operators, and quantum expectation values are calculated for generic two-mode squeezed states characterized by a squeezing parameter r and a squeezing angle phi. Allowing for generic values of the squeezing angle is especially relevant when phi is not under experimental control, such as in cosmic inflation, where small quantum fluctuations in the early universe are responsible for structures formation. Compared to previous studies restricted to phi = 0 and to a fixed orientation of the pseudo-spin operators, allowing for phi = 0 and optimizing the angular configuration leads to a completely new and rich phenomenology. Two dual schemes of approximation are designed that allow for comprehensive exploration of the squeezing parameter space. In particular, it is found that Bell inequalities can be violated when the squeezing parameter r is large enough, r greater than or similar to 1.12, and the squeezing angle phi is small enough, phi less than or similar to 0.34 e(-r).