Inseparability of mixed two-mode Gaussian states generated with a SU(1,1) interferometer

We study the entanglement properties of two-mode Gaussian light emerging from a generic SU (1, 1) interferometer. Our tool is the two-mode characteristic function which is determined by the 4 x 4 covariance matrix. Por an initial product of two mixed single-mode Gaussian states we investigate the output two-mode covariance matrix. Its structure displays the noise properties of the reduced states as well as the correlations between modes. Classicality of the output two-mode state is characterized by the existence of the Glauber-Sudarshan P representation. For testing separability we apply the Peres-Simon criterion requiring preservation of the positivity of the density matrix under partial transposition. Since inseparability entails nonclassicality, the threshold gain above which nonclassicality of the output state becomes manifest is lower than that allowing for its inseparability. We find that only for a thermal input do nonclassicality and inseparability of the output have the same threshold gain.