  We determine the theoretical limits to squeezing-enhanced measurement
sensitivity of mechanical motion in a cavity optomechanical system. The motion
of a mechanical resonator is transduced onto quadrature fluctuations of a
cavity optical field and a measurement is performed on the optical field
exiting the cavity. We compare measurement sensitivities obtained with coherent
probing and quantum-enhanced probing of the mechanical motion, i.e. the
coherent probe field carries vacuum states and quadrature squeezed vacuum
states at sideband frequencies, respectively. We find that quantum-enhanced
probing provides little to no improvement in motion sensing for resonators in
the unresolved sideband regime but may significantly increase measurement
sensitivities for resonators in the resolved sideband regime.
