We show how to apply the Leggett-Garg inequality to opto-electro-mechanical systems near their quantum ground state. We find that by using a dichotomic quantum non-demolition measurement (via, e.g., an additional circuit-QED measurement device) eithe
r on the cavity or on the nanomechanical system itself, the Leggett-Garg inequality is violated. We argue that only measurements on the mechanical system itself give a truly unambigous violation of the Leggett-Garg inequality for the mechanical system. In this case, a violation of the Leggett-Garg inequality indicates physics beyond that of macroscopic realism is occurring in the mechanical system. Finally, we discuss the difficulties in using unbound non-dichotomic observables with the Leggett-Garg inequality.
