We show how to apply the Leggett-Garg inequality to opto-electro-mechanicalsystems near their quantum ground state. We find that by using a dichotomicquantum non-demolition measurement (via, e.g., an additional circuit-QEDmeasurement device) either on the cavity or on the nanomechanical systemitself, the Leggett-Garg inequality is violated. We argue that onlymeasurements on the mechanical system itself give a truly unambigous violationof the Leggett-Garg inequality for the mechanical system. In this case, aviolation of the Leggett-Garg inequality indicates physics beyond that of"macroscopic realism" is occurring in the mechanical system. Finally, wediscuss the difficulties in using unbound non-dichotomic observables with theLeggett-Garg inequality.
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