  Quantum discord, a measure of genuinely quantum correlations, is generalized
to continuous variable systems. For all two-mode Gaussian states, we calculate
analytically the quantum discord and a related measure of classical
correlations, solving an optimization over all Gaussian measurements. Almost
all two-mode Gaussian states are shown to have quantum correlations, while for
separable states, the discord is smaller than unity. For a given amount of
entanglement, it admits tight upper and lower bounds. Via a duality between
entanglement and classical correlations, we derive a closed formula for the
Gaussian entanglement of formation of all mixed three-mode Gaussian states
whose normal mode decomposition includes two vacua.
