  Interaction with a thermal environment decoheres the quantum state of a
mechanical oscillator. When the interaction is sufficiently strong, such that
more than one thermal phonon is introduced within a period of oscillation,
quantum coherent oscillations are prevented. This is generally thought to
preclude a wide range of quantum protocols. Here, we introduce a pulsed
optomechanical protocol that allows ground state cooling, general linear
quantum non-demolition measurements, optomechanical state swaps, and quantum
state preparation and tomography without requiring quantum coherent
oscillations. Finally we show how the protocol can break the usual thermal
limit for sensing of impulse forces.
