Part I: Optomechanical systems subjected to environmental noise give rise to rich physical phenomena. We investigate entanglement between a mechanical oscillator and the reflected coherent optical field in a general, not necessarily Markovian environment. For the input optical field, we consider stationary Gaussian states and frequency-dependent squeezing. We demonstrate that for a coherent laser drive, either unsqueezed or squeezed in a frequency-independent manner, optomechanical entanglement is destroyed after a threshold that depends only on the environmental noises---independent of the coherent coupling between the oscillator and the optical field, or the squeeze factor. In this way, we have found a universal entangling-disentangling transition. We also show that for a configuration in which the oscillator and the reflected field are separable, entanglement cannot be generated by incorporating frequency-dependent squeezing in the optical field.

Part II: Given some Gaussian, quantum channel acting on a bipartite state, how well can we approximate it by using only local operations and classical communication (LOCC)? To answer this question, we find the fidelity-maximizing LOCC channel. Then, we explore strategies where the LOCC fidelity is minimal, i.e. the channel cannot be accurately represented with only LOCC operations. In the context of gravitational interaction, these results provide a pathway for experimental verification of the quantum nature of gravity in the low-energy limit.