Gravity with its lack of background structures, as described by GR, has presented serious difficulty to any attempt to quantization. These difficulties have also led to the idea that gravity could be entirely classical, that quantum mechanics needs to be deeply modified in view of QG, or that quantizing gravity could be a not well-posed problem to start with.
Quantum Superposition of Massive Objects and the Quantization of Gravity
While the majority of physicists working in Quantum Gravity or High-energy physics would certainly say that gravity ought to be quantum and quantized as the other fundamental forces, this is not a proven fact.
It is indeed not a case that R. Feynman (see e.g. here and references therein) went through proposing gedankenexperiments that, once carried out, would have been able to prove (or not) if gravity presents quantum features, independently on the preferred theory of quantum gravity. Nowadays we are still at the same point. However, many recent proposals for near-future experiments able to test quantum aspects of gravity have been put forward and they employ interesting new quantum technologies.
In [Belenchia et. al, Phys. Rev. D 98, 126009 (2018). arXiv: 1807.07015] we analyze a gedankenexperiment involving massive objects in a quantum superposition of different locations and their gravitational field. We prove that, for consistency with causality and quantum complementary, the gravitational field of linearized gravity should have a quantum field description. In a subsequent essay [Belenchia et al. IJMPD Vol. 28, No. 14, 1943001 (2019).arXiv:1905.04496 ], we further investigate the role of quantum information in the aforementioned Gedankenexperiment.
There are several situation in which the combination of relativistic and quantum concepts can lead to unexpected and exciting possibilities. This is the case for the physics of quantum clocks and indefinite causal structure.
Time reference frames and gravitating quantum clocks
In [Castro-Ruiz et al., Nat Commun11, 2672 (2020)], we investigate this fascinating topic for what concerns the time localizability of spacetime events and the physics of quantum clocks. We develop a framework for “time reference frames,” in which events are defined in terms of quantum operations with respect to a quantum clock. We find that, when clocks and quantum systems interact gravitationally, the temporal localisability of events becomes relative, depending on the time reference frame.
Quantum Temporal Superposition: the case of QFT
In this work, we consider instead what happens when a quantum-controlled superposition of particle detectors at different space-time points is used to probe the correlations of a quantum field. We show that, due to quantum interference effects, two detectors can gain information on field correlations which would not be otherwise accessible, with relevant consequences for information-theoretic quantities, like entanglement and mutual information.