  One of the outstanding questions in modern physics is how to test whether
gravity is classical or quantum in a laboratory. Recently there has been a
proposal to test the quantum nature of gravity by creating quantum
superpositions of two nearby neutral masses, close enough that the quantum
nature of gravity can entangle the two quantum systems, but still sufficiently
far away that all other known Standard Model interactions remain negligible.
However, the mere process of preparing superposition states of a neutral mass
(the light system), requires the vicinity of laboratory apparatus (the heavy
system). We will suppose that such a heavy system can be modelled as another
quantum system; since gravity is universal, the lighter system can get
entangled with the heavier system, providing an inherent source of
gravitational decoherence. In this paper, we will consider two light and two
heavy quantum oscillators, forming pairs of probe-detector systems, and study
under what conditions the entanglement between two light systems evades the
decoherence induced by the heavy systems. We conclude by estimating the
magnitude of the decoherence in the proposed experiment for testing the quantum
nature of gravity.
