  The pairwise quantum correlations in a tripartite optomechanical system
comprising a mechanical mode and two optical modes are analyzed. The Simon
criterion is used as a witness of the separability. Whereas, the Gaussian
discord is employed to capture the quantumness of correlations. Both
entanglement and Gaussian discord are evaluated as functions of the parameters
characterizing the environment and the system (temperature, squeezing and
optomechanical coupling). We work in the resolved-sideband regime. We show that
it is possible to reach simultaneous three bipartite entanglements via the
quantum correlations transfer from the squeezed light to the system. While,
even without squeezed light, the quantumness of correlations can be captured
simultaneously between the three modes for a very wide range of parameters.
Specifically, we find that the two optical modes exhibit more quantum
correlations in comparison with the entangled mechanical-optical modes.
Finally, unlike the two hybrid subsystems, the purely optical one seems more
resilient against the environmental destructive effects.
