  We discuss a scheme for macrorealistic theories of the Leggett-Garg form [A.
J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)]. Our scheme is based
on a hybrid optomechanical system. It seems reasonable to test these
inequalities with an optomechanical system, since in an optomechanical cavity
it is possible to create non-classical states of the mirror through a
projective measurement on the cavity field. We will present the protocol to
generate such non-classicality for a general optomechanical cavity and after we
will carry out a theoretical test for one of the possible formulations of these
inequalities using a hybrid optomechanical system. Specifically, the inequality
will be investigated for an harmonic oscillator coupled to a two-level system,
which replaces the light field of the cavity. The aim is to reproduce, with
this system, the evolution of a single spin-1/2 for which the inequality is
violated; this is achievable through the conditioning of the two-level system
which will be used as an ancilla.
