Abstract The effect of gravity is a key factor in understanding the physical phenomenon. Quantizing gravity is challenging task due to weak interactions of gravity in quantum world. The quantum nature of gravity can be witnessed by entanglement in an interferometric platform Phys. Rev. D 105, 086024 (2022). A natural question arises concerning whether the quantization of gravity can be observed via other means. In this work, we propose an effective approach to witnessing the gravity-induced quantumness by quantum uncertainty relations, including entropy-based and coherence-based uncertainty relations. The theoretical frameworks for wave-particle, entropic uncertainty and coherence are established, which can prove the quantum nature of gravity. The three-measurement entropic uncertainty and coherence exhibit the oscillatory features for the gravity-induced phases in the interferometric scheme. It is found that the evolutionary dynamics of coherence is inversely correlated with the measured uncertainty. It can be interpreted that the reduction of systemic quantum resource leads to the increase of entropic uncertainty, and vice versa. When the entropic uncertainty reaches zero, systemic coherence is the maximum value, providing a viable physical explanation for the gravity-induced quantumness. It shows that the entropic uncertainty and coherence can be regarded as the reliable indicators for capturing the gravity-induced quantumness. Compared to entanglement-based gravity quantization scheme, it shows that the capabilities are equivalent for detecting the gravity-induced quantumness using entropy uncertainty, coherence, and entanglement. The results could lay a solid theoretical foundation for the potential applications of quantum gravity in quantum information science.
Ming et al. (Wed,) studied this question.