  We study the transfer of quantum correlations between two movable mirrors of
two Fabry-P\'erot cavities separated via broadband squeezed light and coupled
via photon hopping process. We investigate the transfer of quantum correlations
from EPR entangled squeezed light to the movable mirrors. We show that Gaussian
quantum steering remains lower than entanglement. We employ Gaussian quantum
steering to characterize the steerability between the two mechanical modes. The
logarithmic negativity is used as the witness of quantum entanglement and
Gaussian quantum discord gives the measure of all non classical correlations
including entanglement. We conclude that the transfer of quantum correlations
is optimal for a strong optomechanical coupling and decreases with the thermal
effects. We also conclude that steering, entanglement and discord are directly
related to photon hopping coupling and the squeezing parameter.

Quantum Physics