  In this Letter we exploit the recently-solved conjecture on the bosonic
minimum output entropy to show the optimality of Gaussian discord, so that the
computation of quantum discord for bipartite Gaussian states can be restricted
to local Gaussian measurements. We prove such optimality for a large family of
Gaussian states, including all two-mode squeezed thermal states, which are the
most typical Gaussian states realized in experiments. Our family also includes
other types of Gaussian states and spans their entire set in a suitable limit
where they become Choi-matrices of Gaussian channels. As a result, we
completely characterize the quantum correlations possessed by some of the most
important bosonic states in quantum optics and quantum information.
