Semi-Classical Model of Detector Efficiency in the Context of Bipartite Gravitational-Wave Detection

Current research into the quantization of gravity has focused primarily on single-point graviton detections. This approach neglects non-classical properties that arise from entanglement between gravitons whose arrivals are coincident at separate detector sites. In developing a bipartite quantum-mechanical framework for the detection of gravitational waves, a necessary step is to characterize detector efficiency for graviton particles. Utilizing the geodesic deviation equation, we construct a model of the detector's departure from free fall in flat spacetime. This model enables us to compute the mean graviton number registered by a single detector, providing a semi-classical measure of effective detector efficiency. We find that low detector efficiency results in resolvable measurement-induced entanglement in bipartite gravitational-wave detections. This work follows up on ``Measurement-induced entanglement entropy of gravitational wave detections'' (Physics Letters B, 2025) by Preston Jones, Quentin G. Bailey, Andri Gretarsson and Edward Poon, which states that low theoretical efficiencies present a challenge for detecting production-induced entanglement. In contrast, for bipartite detections of gravitational waves involving measurement-induced entanglement, the entanglement occurs at the time of measurement. Low detector efficiencies therefore become an asset for revealing non-classical signatures, since quantum effects are more prominent as a result of the reduced graviton number associated with low detector efficiency.