Bipartite temporal Bell inequalities for two-mode squeezed states

Bipartite temporal Bell inequalities are similar to the usual Bell inequalities except that, instead of changing the direction of the polariser at each measurement, one changes the time at which the measurement is being performed. By doing so, one is able to test for realism and locality, but relying on position measurements only. This is particularly useful in experimental setups where the momentum direction cannot be probed (such as in cosmology for instance). We study these bipartite temporal Bell inequalities for continuous systems placed in two-mode squeezed states, and find some regions in parameter space where they are indeed violated. We highlight the role played by the rotation angle, which is one of the three parameters characterising a two-mode squeezed state (the other two being the squeezing amplitude and the squeezing angle). In single-time measurements, it only determines the overall phase of the wavefunction and can therefore be discarded, but in multiple-time measurements, its time dynamics becomes relevant and crucially determines when bipartite temporal Bell inequalities can be violated. Our study opens up the possibility of new experimental designs for the observation of Bell inequality violations.