Testing Bell inequalities with photon-subtracted Gaussian states

Abstract

Recently, photon subtracted Gaussian states (PSGSs) were generated by several experimental groups. Those states were called "Schr\"odinger kittens" due to their similarities to superpositions of coherent states (SCSs) with small amplitudes. We compare the ideal SCSs and the PSGSs for experimental tests of certain types of Bell inequalities. In particular, we analyze the effects of the key experimental components used to generate PSGSs: mixedness of the Gaussian states, limited transmittivity of the beam splitter and the avalanche photodetector which cannot resolve photon numbers. As a result of this analysis, the degrees of mixedness and the beam splitter transmittivity that can be allowed for successful tests of Bell inequalities are revealed.