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We study general quantum correlations of continuous variable Gaussian statesand their interplay with entanglement. Specifically, we investigate theexistence of a quantum protocol activating all nonclassical correlationsbetween the subsystems of an input bipartite continuous variable system, intooutput entanglement between the system and a set of ancillae. For inputGaussian states, we prove that such an activation protocol cannot beaccomplished with Gaussian operations, as the latter are unable to create anyoutput entanglement from an initial separable yet nonclassical state in aworst-case scenario. We then construct a faithful non-Gaussian activationprotocol, encompassing infinite-dimensional generalizations of controlled-NOTgates to generate entanglement between system and ancillae, in direct analogywith the finite-dimensional case. We finally calculate the negativity ofquantumness, an operational measure of nonclassical correlations defined interms of the performance of the activation protocol, for relevant classes oftwo-mode Gaussian states.

No-activation theorem for Gaussian nonclassical correlations by Gaussian operations