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arXiv:2401.03867 · Physical review. D/Physical review. D.

Quantumness of the gravitational field: A perspective on monogamy relation

Yuuki Sugiyama, Akira Matsumura, Kazuhiro Yamamoto

Published Aug 19, 2024• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevd.110.045016

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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.
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.
When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with other massive bodies via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. Thus, a Newtonian-like gravitational field must be capable of carrying quantum information. Our analysis supports the view that table-top experiments testing entanglement of systems interacting via gravity do probe the quantum nature of gravity, even if no “gravitons” are emitted during the experiment.
The aim of this article is to provide an introduction to the use of quantum information methods for investigating the interface between quantum theory and gravity. To this end, we discuss the basic principles of two current research streams that use this approach. The first one explores a phenomenon known as gravitationally induced entanglement, which aims to infer whether the gravitational field responsible for the interaction between two massive bodies must be quantized or not. The second stream investigates causal structures, thereby providing indirect evidence that spacetime may exhibit non-classical behavior. Before presenting these topics, we briefly review some fundamental concepts and experiments from quantum information theory, such as the Mach-Zehnder interferometer, the Stern-Gerlach experiment, Bell inequalities and entanglement, and the language of quantum circuits.
We analyze the dynamics of a gravity-induced entanglement for NNN massive particles. Considering the linear configuration of these particles, we investigate the entanglement between a specific pair of particles under the influence of the gravitational interaction between the massive particles. As the particle number increases, the specific particle pair decoheres more easily due to the gravitational interaction with other particles. The timescale of the gravity-induced decoherence is analytically determined. We also discuss the entanglement dynamics of initially entangled particles, which exemplify the monogamy of the gravity-induced entanglement.
We develop a quantum field-theoretic model of gravitationally induced entanglement (GIE) between two massive objects in spatial superposition. The masses are described as excitations of a scalar field in an external harmonic potential, allowing for a well-defined notion of relativistic coherent states. Using linearized quantum gravity in the static limit, we derive an effective Hamiltonian that induces entanglement between the field modes occupied by the masses. To probe this entanglement, we construct an observable from field operators that corresponds to the probability density of detecting the center of mass of one of these massive objects. Using this, we compute the fringe visibility in the overlap region and find that gravitationally induced entanglement leads to a decrease in visibility, consistent with previous nonrelativistic results. Additionally, we identify relativistic corrections that accelerate the decay of fringe visibility. These results provide a framework for studying weakly relativistic quantum field systems and their gravitational interactions in tabletop experiments.
Abstract What gravitational field is generated by a massive quantum system in a spatial superposition? Despite decades of intensive theoretical and experimental research, we still do not know the answer. On the experimental side, the difficulty lies in the fact that gravity is weak and requires large masses to be detectable. However, it becomes increasingly difficult to generate spatial quantum superpositions for increasingly large masses, in light of the stronger environmental effects on such systems. Clearly, a delicate balance between the need for strong gravitational effects and weak decoherence should be found. We show that such a trade off could be achieved in an optomechanics scenario that allows to witness whether the gravitational field generated by a quantum system in a spatial superposition is in a coherent superposition or not. We estimate the magnitude of the effect and show that it offers perspectives for observability.