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Utilizing the tools of quantum optics to prepare and manipulate quantum states of motion of a mechanical resonator is currently one of the most promising routes to explore non-classicality at a macroscopic scale. An important quantum optomechanical tool yet to be experimentally demonstrated is the ability to perform complete quantum state reconstruction. Here, after providing a brief introduction to quantum states in phase space, we review and contrast the current proposals for state reconstruction of mechanical motional states and discuss experimental progress. Furthermore, we show that mechanical quadrature tomography using back-action-evading interactions gives an $s$-parameterized Wigner function where the numerical parameter $s$ is directly related to the optomechanical measurement strength. We also discuss the effects of classical noise in the optical probe for both state reconstruction and state preparation by measurement.
Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a r
Quantum teleportation, the faithful transfer of an unknown input state onto a remote quantum system, is a key component in long distance quantum communication protocols and distributed quantum computing. At the same time, high frequency nano-optomech
Quantum optical measurement techniques offer a rich avenue for quantum control of mechanical oscillators via cavity optomechanics. In particular, a powerful yet little explored combination utilizes optical measurements to perform heralded non-Gaussia
We propose a scheme for the generation of a robust stationary squeezed state of a mechanical resonator in a quadratically coupled optomechanical system, driven by a pulsed laser. The intracavity photon number presents periodic intense peaks suddenly
Entanglement generation at a macroscopic scale offers an exciting avenue to develop new quantum technologies and study fundamental physics on a tabletop. Cavity quantum optomechanics provides an ideal platform to generate and exploit such phenomena o