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EPR steering is an asymmetric form of correlations which is intermediatebetween quantum entanglement and Bell nonlocality, and can be exploited forquantum communication with one untrusted party. In particular, steering ofcontinuous variable Gaussian states has been extensively studied as amanifestation of the EPR paradox. While most of these studies focused onquadrature measurements for steering detection, two recent works revealed thatthere exist Gaussian states which are only steerable by non-Gaussianmeasurements. In this paper we perform a systematic investigation of EPRsteering of bipartite Gaussian states by pseudospin measurements, complementingand extending previous findings. We first derive the density matrix elements oftwo-mode squeezed thermal states in the Fock basis, which may be of independentinterest. We then use such a representation to investigate steering of thesestates as detected by a nonlinear criterion, based on second moments of thepseudospin correlation matrix. This analysis reveals previously unexploredregimes where non-Gaussian measurements are more effective than Gaussian onesto witness steering of Gaussian states in the presence of local noise. Wefurther consider an alternative set of pseudospin observables, whoseexpectation value can be expressed compactly in terms of Wigner functions forall two-mode Gaussian states. However, according to the adopted criterion,these observables are found to be always less sensitive than Gaussianobservables for steering detection. Finally, we investigate continuous variableWerner states, which are non-Gaussian mixtures of Gaussian states, and findthat pseudospin measurements are always more effective than Gaussian ones toreveal their steerability. Our results provide useful insights on the role ofnon-Gaussian measurements in characterizing quantum correlations of Gaussianand non-Gaussian states.

Investigating Einstein-Podolsky-Rosen steering of continuous variable bipartite states by non-Gaussian pseudospin measurements