  The optomechanical state transfer protocol provides effective, lossy, quantum
beam-splitter-like dynamics where the strength of the coupling between the
electromagnetic and mechanical modes is controlled by the optical steady-state
amplitude. By restricting to a subspace with no losses, we argue that the
transition from mode-hybridization in the strong coupling regime to the
damped-dynamics in the weak coupling regime, is a signature of the passive
parity-time ($\mathcal{PT}$) symmetry breaking transition in the underlying
non-Hermitian quantum dimer. We compare the dynamics generated by the quantum
open system (Langevin or Lindblad) approach to that of the
$\mathcal{PT}$-symmetric Hamiltonian, to characterize the cases where the two
are identical. Additionally, we numerically explore the evolution of separable
and correlated number states at zero temperature as well as thermal initial
state evolution at room temperature. Our results provide a pathway for
realizing non-Hermitian Hamiltonians in optomechanical systems at a quantum
level.
