  Entanglement generation by Newtonian gravitational potential between objects
has been widely discussed to reveal the quantum nature of gravity. In this
paper, we perform a quantum field theoretical analysis of a slightly modified
version of the gedanken experiment by Mari and co-workers. We show that
decoherence due to the presence of a detector propagates with the speed of
light in terms of a retarded Green's function, as it should be consistent with
causality of relativistic field theories. The quantum nature of fields, such as
quantum fluctuations or emission of gravitons expressed in terms of the Keldysh
Green's function also play important roles in the mechanism of decoherence due
to on-shell particle creation. We also discuss the trade-off relation between
the visibility of the interference and the distinguishability of the
measurement, known as the wave particle duality, in our setup.
