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Entanglement generation by Newtonian gravitational potential between objectshas been widely discussed to reveal the quantum nature of gravity. In thispaper, we perform a quantum field theoretical analysis of a slightly modifiedversion of the gedanken experiment by Mari and co-workers. We show thatdecoherence due to the presence of a detector propagates with the speed oflight in terms of a retarded Green's function, as it should be consistent withcausality of relativistic field theories. The quantum nature of fields, such asquantum fluctuations or emission of gravitons expressed in terms of the KeldyshGreen's function also play important roles in the mechanism of decoherence dueto on-shell particle creation. We also discuss the trade-off relation betweenthe visibility of the interference and the distinguishability of themeasurement, known as the wave particle duality, in our setup.

Complementarity and causal propagation of decoherence by measurement in relativistic quantum field theories