High-dimensional Bell test for a continuous variable state in phase space and its robustness to detection inefficiency

We propose a scheme for testing high-dimensional Bell inequalities in phase space. High-dimensional Bell inequalities can be recast into the forms of a phase-space version using quasiprobability functions with the complex-valued order parameter. We investigate their violations for two-mode squeezed states while increasing the dimension of measurement outcomes, and finally show the robustness of high-dimensional tests to detection inefficiency.