Investigating the quantum nature of gravity is an important issue in modern physics. Recently, studies pertaining to the quantum superposition of gravitational potential have garnered significant interest. Inspired by Mari et al. [Sci. Rep. 6, 22777 (2016)] and Baym and Ozawa [Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009)], Belenchia et al. [Phys. Rev. D 98, 126009 (2018)] considered a gedanken experiment involving such a quantum superposition and mentioned that the superposition renders causality and complementarity inconsistent. They resolved this inconsistency by considering the quantized dynamical degrees of freedom of gravity. This suggests a strong relationship between the quantum superposition of the gravitational potential and the quantization of the gravitational field. In our previous study [Phys. Rev. D 106, 125002 (2022)], we have shown that the quantum uncertainty of a field guarantees the consistency between causality and complementarity. In this study, we focus on the entanglement between two particles' states due to the electromagnetic/gravitational potential and investigate its relationship with quantum uncertainty, causality, and complementarity. Our numerical analyses show that the quantum uncertainty of the electromagnetic/gravitational field results in vacuum fluctuations and prohibits the entanglement between two particles' states when causality is satisfied. We further demonstrate that complementarity holds when the particles do not get entangled. The uncertainty relation does not cause the entanglement between two particles' states, which guarantees complementarity.
Investigating the quantum nature of gravity is an important issue in modern physics. Recently, studies pertaining to the quantum superposition of gravitational potential have garnered significant interest. Inspired by Mari et al. [Sci. Rep. 6, 22777 (2016)] and Baym and Ozawa [Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009)], Belenchia et al. [Phys. Rev. D 98, 126009 (2018)] considered a gedanken experiment involving such a quantum superposition and mentioned that the superposition renders causality and complementarity inconsistent. They resolved this inconsistency by considering the quantized dynamical degrees of freedom of gravity. This suggests a strong relationship between the quantum superposition of the gravitational potential and the quantization of the gravitational field. In our previous study [Phys. Rev. D 106, 125002 (2022)], we have shown that the quantum uncertainty of a field guarantees the consistency between causality and complementarity. In this study, we focus on the entanglement between two particles' states due to the electromagnetic/gravitational potential and investigate its relationship with quantum uncertainty, causality, and complementarity. Our numerical analyses show that the quantum uncertainty of the electromagnetic/gravitational field results in vacuum fluctuations and prohibits the entanglement between two particles' states when causality is satisfied. We further demonstrate that complementarity holds when the particles do not get entangled. The uncertainty relation does not cause the entanglement between two particles' states, which guarantees complementarity.
It has long been debated whether gravity should be quantized or not. Recently, the authors in [Sci. Rep. 6, 22777 (2016); Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009)] discussed the inconsistency between causality and complementarity in a Gedankenexperiment involving the quantum superposition of massive/charged bodies, and Belenchia et al. [Phys. Rev. D 98, 126009 (2018); Int. J. Mod. Phys. D 28, 1943001 (2019)] resolved the inconsistency by requiring the quantum radiation and vacuum fluctuations of gravitational/electromagnetic field. Stimulated by their works, we reanalyze the consistency between the two physical properties, causality and complementarity, according to the quantum field theory. In this analysis, we consider a Gedankenexperiment inspired by [Sci. Rep. 6, 22777 (2016); Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009); Phys. Rev. D 98, 126009 (2018); Int. J. Mod. Phys. D 28, 1943001 (2019)], in which two charged particles coupled with a photon field are in a superposition of two trajectories. First, we observe that causality is satisfied by the retarded propagation of the photon field. Next, by introducing an inequality between visibility and which-path information, we show that the quantum radiation and vacuum fluctuations of the photon field ensure complementarity. We further find that the Robertson inequality associated with the photon field leads to the consistency between causality and complementarity in our Gedankenexperiment. Finally, we mention that a similar feature appears in the quantum field of gravity.
Understanding the phenomenon of quantum superposition of gravitational fields induced by massive quantum particles is an important starting point for quantum gravity. The purpose of this study is to deepen our understanding of the phenomenon of quantum superposition of gravitational fields. To this end, we consider a trade-off relation of entanglement (monogamy relation) in a tripartite system consisting of two massive particles and a gravitational field that may be entangled with each other. Consequently, if two particles cannot exchange information mutually, they are in a separable state, and the particle and gravitational field are always entangled. Furthermore, even when two particles can send information to each other, there is a trade-off between the two particles and the gravitational field. We also investigate the behavior of the quantum superposition of the gravitational field using quantum discord. We find that quantum discord increases depending on the length scale of the particle superposition. Our results may help understand the relationship between the quantization of the gravitational field and the meaning of the quantum superposition of the gravitational field.
We analyze a Gedankenexperiment previously considered by Mari et al. [Sci. Rep. 6, 22777 (2016).] that involves quantum superpositions of charged and/or massive bodies (``particles'') under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alice's particle) and vacuum fluctuations of the electromagnetic field (which limits Bob's ability to localize his particle to better than a charge-radius), both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this Gedankenexperiment. We correct an error in the analysis of Mari et al. [Sci. Rep. 6, 22777 (2016).] and of Baym and Ozawa [Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009).], who did not properly account for the conservation of center of mass of an isolated system. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case, provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description.
Belenchia et al. [Phys. Rev. D 98, 126009 (2018)] have analyzed a gedankenexperiment where two observers, Alice and Bob, attempt to communicate via superluminal signals using a superposition of massive particles dressed by Newtonian fields and a test particle as field detector. Quantum fluctuations in the particle motion and in the field prevent signaling or violations of quantum mechanics in this setup. We reformulate this thought experiment by considering gravitational waves emitted by an extended quadrupolar object as a detector for Newtonian tidal fields. We find that quantum fluctuations in the gravitational waves prevent signaling. In the Newtonian limit, rotating black holes behave as extended quadrupolar objects, as consequence of the strong equivalence principle. It follows that consistency of the Newtonian limit of general relativity with quantum mechanics requires the quantization of gravitational radiation, even when the waves originate in strong gravity sources.
The quantization of gravity remains one of the most important---yet extremely elusive---challenges at the heart of modern physics. Any attempt to resolve this long-standing problem seems to be doomed, as the route to any direct empirical evidence (i.e., detecting gravitons) that sheds light on the quantum aspect of gravity is far beyond the current capabilities. Recently, it was discovered that gravitationally induced entanglement, tailored in the interferometric frameworks, can be used to witness the quantum nature of gravity. Even though these schemes offer promising tools for investigating quantum gravity, many fundamental and empirical aspects of the schemes are yet to be discovered. Considering the fact that, besides quantum entanglement, the quantum uncertainty and complementarity principles are the two other foundational aspects of quantum physics, the quantum nature of gravity needs to manifest all of these features. Here, we lay out an interferometric platform for testing these nonclassical aspects of quantum mechanics in the quantum gravity setting, which connects gravity and quantum physics in a broader and deeper context. As we show in this work, all of these fundamental features of quantum gravity can be framed and thoroughly analyzed in an interferometric scheme.
In recent years, the quantum nature of gravity has attracted significant attention as one of the most important problems in modern physics. Here, we analyze the mechanism of gravitationally-induced entanglement from the perspective of quantum resource theory. Building on the framework of Bose et al. [Phys. Rev. Lett. 119, 240401 (2017)], we show that the gravitational interaction acts as a unitary channel, redistributing quantum resources between two spatially superposed masses. Specifically, we demonstrate that the resulting bipartite entanglement originates from the coherent conversion of local quantum coherence -- initially present in each subsystem -- into shared non-local correlations. We derive exact, analytical complementarity relations quantifying this conversion, link the decay of local coherence directly to the growth of entanglement, and support these findings with numerical simulations. Our results clarify the underlying mechanism and establish gravity as a coherence-to-entanglement conversion channel, offering a refined interpretive basis for forthcoming experimental tests. Crucially, we show that initial coherence is a necessary condition for entanglement generation and that its degree bounds the maximum achievable entanglement, with maximal entanglement requiring initial maximal coherence.