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

TL;DR

This paper analyzes how decoherence propagates causally in relativistic quantum field theories, emphasizing the roles of quantum fluctuations, graviton emission, and the wave-particle duality in a modified gravitational entanglement experiment.

Contribution

It demonstrates that decoherence propagates at the speed of light via retarded Green's functions and highlights the quantum field effects influencing decoherence mechanisms.

Findings

Decoherence propagates with the speed of light in relativistic theories.

Quantum fluctuations and graviton emission significantly affect decoherence.

A trade-off exists between interference visibility and measurement distinguishability.

Abstract

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.