Schwinger effect of Gaussian correlations in constant electric fields

We study the Schwinger effect of Gaussian correlations (quantum entanglement, discord and mutual information) of the continuous-variable two-mode squeezed states shared by Alice and Bob, paying special attention to the difference of the Schwinger effect of correlations between modes of fermion-fermion and qubit-bosonic fields studied previously. We also study the redistribution and conservativeness of the correlations under the Schwinger effect.