  We introduce a scheme to reconstruct an arbitrary quantum state of a
mechanical oscillator network. We assume that a single element of the network
is coupled to a cavity field via a linearized optomechanical interaction, whose
time dependence is controlled by a classical driving field. By designing a
suitable interaction profile, we show how the statistics of an arbitrary
mechanical quadrature can be encoded in the cavity field, which can then be
measured. We discuss the important special case of Gaussian state
reconstruction, and study numerically the effectiveness of our scheme for a
finite number of measurements. Finally, we speculate on possible routes to
extend our ideas to the regime of single-photon optomechanics.
