  Momentum diffusion is a possible mechanism for driving macroscopic quantum
systems towards classical behaviour. Experimental tests of this hypothesis rely
on a precise estimation of the strength of this diffusion. We show that
quantum-mechanical squeezing offers significant improvements, including when
measuring position. For instance, with 10dB of mechanical squeezing,
experiments would require a tenth of proposed free-fall times. Momentum
measurement is better by an additional factor of three, while another
quadrature is close to optimal. These have particular implications for the
space-based MAQRO proposal -- where it could rule out the spontaneous collapse
theory due to Ghirardi, Rimini, and Weber -- as well as terrestrial
optomechanical sensing.
