Einstein-Podolsky-Rosen steering in symmetrical Gaussian states

We have explored quantum Einstein-Podolsky-Rosen steering in symmetric two-mode Gaussian states using Gaussian and non-Gaussian measurements. For Gaussian measurements, we show that steering between the output modes of a symmetric beam splitter is possible regardless of purity when a threshold input-state quadrature variance compression is achieved. Using the non-Gaussian operators introduced in Ji et al. [Sci. Rep. 6, 29729 (2016)] we show that non-Gaussian measurements can outperform Gaussian measurements for symmetrical states. We also analyze the possibility of asymmetric measurements setups made possible by non-Gaussian measurements and provide examples where such asymmetry is optimal for revealing steering.