“…As non-Gaussian continuous-variable states have rich structures in the phase space, it is important to explore possibility of efficient Bell inequality tests using those states. Among non-Gaussian continuous-variable states, superpositions of two coherent states (SCSs) [10,11] in free-traveling optical fields have been found a very useful tool for fundamental tests of quantum theory [12,13,14,15,16,17] as well as for quantum information applications [18,19,20,21,22,23]. In particular, they are useful for Bell inequality tests using various measurements such as photon on/off detection, photon number detection, and homodyne detection [12,13,14,15].…”