We show that the atom interferometric coherence revival test suggested in [arXiv:2101.11629 [quant-ph] (2021)] does not test the quantum nature of the gravitational field when the atoms are coupled to a mechanical oscillator prepared in a thermal state. Specifically we clarify that the same coherence revivals take place in a model where the atoms are coupled to a classical oscillator through a classical gravitational field. We further elucidate the quantum mechanical calculation, showing that entanglement is not the source of the revivals. The suggested test is thus only relevant for pure initial quantum states of the oscillator. In this regime, numerical estimates show that it is unfeasible to do a test of the proposed type.
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