  We demonstrate a complete, probabilistic quantum dynamical simulation of the
standard nonlinear Hamiltonian of optomechanics, including decoherence at
finite temperatures. Robust entanglement of an optical pulse with the
oscillator is predicted, as well as strong quantum steering between the optical
and mechanical systems. Importantly, our probabilistic quantum simulation
method uses the positive-P technique, which is scalable to large Hilbert
spaces.
