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Quantum State Gravity Entanglement Spectrum

Jincheng Zhang

Published Aug 17, 2026• 0 citations
Publisher

Abstract

This paper introduces the Quantum State Gravity Entanglement Spectrum (QSGES) – a novel framework for investigating the potential influence of gravity on quantum entanglement. Current research focuses on entanglement spectra and exploring gravitational effects, often treating them as separate phenomena. We propose that quantum states can be linked through a previously unrecognized structure: gravitational entanglement. This structure is represented mathematically as the QSGES, denoted as [Sgq(ω)], which quantifies the correlation strength between a quantum state and a gravitational field. The theoretical foundation of the QSGES relies on a reinterpretation of entanglement, suggesting that it may be fundamentally intertwined with gravitational forces at the quantum level. We outline a conceptual experiment – a large-scale quantum superposition experiment involving massive objects – designed to potentially observe this gravitational entanglement. The development of QSGES represents a potentially Nobel-worthy breakthrough, offering the first empirical evidence for the direct influence of gravity on quantum entanglement, fundamentally altering our understanding of the universe.

DOI
10.5281/zenodo.21975487

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This paper introduces the Quantum State Gravity Entanglement Spectrum (QSGES) – a novel framework for investigating the potential influence of gravity on quantum entanglement. Current research focuses on entanglement spectra and exploring gravitational effects, often treating them as separate phenomena. We propose that quantum states can be linked through a previously unrecognized structure: gravitational entanglement. This structure is represented mathematically as the QSGES, denoted as [Sgq(ω)], which quantifies the correlation strength between a quantum state and a gravitational field. The theoretical foundation of the QSGES relies on a reinterpretation of entanglement, suggesting that it may be fundamentally intertwined with gravitational forces at the quantum level. We outline a conceptual experiment – a large-scale quantum superposition experiment involving massive objects – designed to potentially observe this gravitational entanglement. The development of QSGES represents a potentially Nobel-worthy breakthrough, offering the first empirical evidence for the direct influence of gravity on quantum entanglement, fundamentally altering our understanding of the universe.
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.
Quantum Gravity Field-Based Probability explores the potential of utilizing quantum entanglement to refine probability calculations within complex quantum systems. The core claim posits the development of a novel framework – the 'Quantum Entanglement Probability Field' – that quantifies the probability of event outcomes by encoding these probabilities within a dynamically evolving field. This represents a departure from classical probability models, offering a potential pathway to improved prediction and a deeper understanding of quantum phenomena. The paper introduces the concept, details the design of the entanglement probability field, and outlines the theoretical and potential experimental implications of this research.
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.
Abstract No experiment to date has provided evidence for quantum features of the gravitational interaction. Recently proposed tests suggest looking for the generation of quantum entanglement between massive objects as a possible route towards the observation of such features. Motivated by advances in optical cooling of mirrors, here we provide a systematic study of entanglement between two masses that are coupled gravitationally. We first consider the masses trapped at all times in harmonic potentials (optomechanics) and then the masses released from the traps. This leads to the estimate of the experimental parameters required for the observation of gravitationally induced entanglement. The optomechanical setup demands LIGO-like mirrors and squeezing or long coherence times, but the released masses can be light and accumulate detectable entanglement in a timescale shorter than their coherence times. No macroscopic quantum superposition develops during the evolution. We discuss the implications from such thought experiments regarding the nature of the gravitational coupling.
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.
The unification of general relativity and quantum mechanics remains one of the most profound challenges in modern theoretical physics. While gravity is exceptionally weak at the microscopic scale, probing its quantum nature requires unprecedented measurement sensitivity. In this paper, we introduce Gravitational Entanglement Phase Microscopy (GEPM), a novel theoretical framework designed to exploit multi-body quantum entanglement to enhance and measure extremely weak gravitational phases. By employing specialized N-body entangled states defined as |Psi_N> = (|0>^N + |1>^N) / sqrt(2), GEPM bypasses the standard quantum limit, scaling the gravitational phase response theoretically with the particle number N through the integrated potential phi_G = (1 / hbar) * integral U_G(t) dt. We outline the fundamental principles of the GEPM framework, the mathematics of collective phase accumulation, the elimination of classical noise interference, and the deep implications for observing genuine quantum gravity signatures.