Gravitationally-Induced Entanglement

Updated 23 October 2025

Gravitationally-induced entanglement is the phenomenon where mutual gravitational interactions induce nonlocal quantum correlations between distinct systems.
Various experimental setups—such as interferometric, optomechanical, and quantum field–theoretic configurations—quantify entangling phases and establish critical parameters for detection.
Observing this entanglement provides practical insights into the quantum nature of gravity and informs the design of sensitive experiments to probe fundamental physics.

Gravitationally-induced entanglement refers to the phenomenon in which two or more quantum systems—such as massive particles, mechanical oscillators, or field modes—become quantum mechanically entangled due to their mutual gravitational interaction. This effect has become a focal point of quantum gravity research, as establishing empirical evidence for the quantum nature of gravity remains a central challenge. A variety of theoretical proposals and experimental designs have been advanced to probe whether gravity, like electromagnetism, can act as a quantum mediator, generating nonlocal quantum correlations between matter systems. Recent developments encompass table-top interferometric setups, optomechanical systems, quantum field–theoretic models, and even many-body and astrophysical scenarios.

1. Fundamental Principles and Theoretical Frameworks

The central principle underlying gravitationally-induced entanglement (GIE) is that any mediator capable of generating entanglement between two local quantum systems must itself possess quantum features; namely, it must be described by non-commuting observables (Marletto et al., 2017). In the canonical "Bose-Marletto-Vedral" (BMV) type proposal, two distinguishable quantum systems (such as mesoscopic particles) are each placed in a spatial superposition, typically implemented via Mach-Zehnder or Stern-Gerlach interferometric techniques. When the gravitational interaction is "active," branch-dependent gravitational phases accumulate. If these phases differ between the four possible spatial configurations, the state of the two systems becomes entangled.

Mathematically, the time-evolved state incorporates gravitationally induced relative phases: $|\Psi\rangle = \frac{1}{2}\Big[|0\rangle|0\rangle + e^{i\phi_1}|0\rangle|1\rangle + e^{i\phi_2}|1\rangle|0\rangle + e^{i(\phi_1 + \phi_2 + \Delta\phi)}|1\rangle|1\rangle\Big]$ where $\phi_i = (G m^2/(\hbar d_i)) \Delta t$ is the phase for a given path separation $d_i$ .

A major quantum information–theoretic result establishes that if the mediator (gravity) is classical (represented by a single observable), then local interactions cannot generate entanglement between the two systems (Marletto et al., 2017). Consequently, the observation of entanglement is often interpreted as indirect evidence that gravity is a quantum channel.

However, the physical interpretation is debated. Some analyses emphasize that the Newtonian potential—responsible for the observed entangling phases—may be derived from constrained classical dynamics (as a "pure gauge" component), leaving open the question of whether the underlying degrees of freedom (e.g., gravitons, the tensor transverse-traceless modes) are genuinely quantum (Anastopoulos et al., 2018, Fragkos et al., 2022).

2. Experimental Configurations and Entanglement Mechanisms

Proposed GIE experiments span mechanical, atomic, optical, and field-theoretic systems. Common strategies include:

Interferometric Massive Particle Setups: Two massive particles in spatial superposition interact gravitationally for time $\Delta t$ ; e.g., Mach-Zehnder arrangements (Marletto et al., 2017).
Optomechanical Arrays: Mechanical oscillators (mirrors or membranes) within optical cavities accumulate gravity-induced cross-Kerr nonlinear phases, which, when the light is in a superposition, lead to photon-photon entanglement (Matsumura et al., 2020).
Released and Trapped Oscillators: In free evolution, gravitational coupling acts through quadratic terms $(x_A - x_B)^2$ , enabling two-mode squeezing and entanglement (Krisnanda et al., 2019).
Quantum Field–Theoretic Schemes: The masses are described as collective excitations (coherent states) of a scalar field. Linearized gravity in the static limit provides an effective interaction Hamiltonian, and field observables (such as projections onto center-of-mass wave packets) serve as entanglement witnesses (Yant et al., 26 Mar 2025).
Many-Body Architectures and Quantum Walks: Generalizing beyond bipartite setups, gravitational interactions are shown to generate multipartite entanglement with time-dependent I-concurrence and, under certain conditions, generalized GHZ-type states (Ghosal et al., 2023); analogous phenomena are modeled in quantum walks (Badhani et al., 2019).
Astrophysical and Curved Spacetime Extensions: GIE effects are modeled in Schwarzschild spacetime, with entanglement collimated by geodesic deviation and orbital parameters (Zhang et al., 2023), and in expanding universes, where spacetime curvature modifies the form of the effective gravitational potential and, correspondingly, the entanglement profile (Brahma et al., 2023).

Within these paradigms, the core dynamical mechanism is the acquisition of path-dependent phases—stemming from the Newtonian or linearized gravitational potential—which, when nontrivial between "branches," yield non-separable quantum states.

3. Key Quantitative Results and Experimental Thresholds

Several works detail quantitative metrics and parameter regimes for observing gravitationally-induced entanglement:

Entangling Phase and Mass/Distance Requirements: The relevant phase follows $\phi \sim (G m_1 m_2 \Delta t)/(\hbar d)$ , implying that, for masses $m \sim 10^{-12}$ – $10^{-17}$ kg and separations $d \sim 1$ $\mu$ m–$10$ $\mu$ m, detectable entanglement requires coherence times $\Delta t$ in the $\mu$ s to ms range (Marletto et al., 2017, Krisnanda et al., 2019, Zhang et al., 13 Apr 2025).
Critical Separation in Classical Gravity Models: The Diòsi–Penrose model (DP) predicts that entanglement can be generated only when the separation $d$ is less than a critical value proportional to the model's fundamental parameter $\sigma$ : $d_c \approx 0.85\sigma$ (standard configuration) or up to $2.21\sigma$ (transversal wave packet spread). Larger separations suppress the entangling effect (Trillo et al., 4 Nov 2024).
Fringe Visibility as an Entanglement Witness: In field-theoretic models, gravitationally induced entanglement manifests as a measurable decrease in interference fringe visibility $\mathcal{V}$ of the center-of-mass position probability. The leading-order reduction is quadratic in the gravitational phase difference between branches (Yant et al., 26 Mar 2025, Yant et al., 2023).
Thermal and Environmental Effects: In thermal settings (e.g., LIGO-like arm endpoints), gravitational interaction via classical GWs still generates entanglement through two-mode squeezing, but thermal effects act as catalysts, causing a hybridization of Bose–Einstein and Maxwell–Boltzmann statistics. Memory-driven time-crystalline phases with quantum memory effects can emerge (Dutta et al., 25 Mar 2025).
Multiparticle and Many-Body Entanglement: For $N$ spatially superposed masses, genuine multipartite (GHZ-type) entanglement is generated if and only if the interaction graph is connected—every bipartition is entangled when corresponding entangling phases do not simultaneously vanish. Values and periodic emergence of GHZ-type entanglement are linked to the structure and ratios of the induced phases (Ghosal et al., 2023).

4. Controversies, Interpretational Ambiguities, and Alternative Theories

The interpretation of GIE as direct evidence for the quantum nature of gravity is subject to scrutiny:

Constraint versus Dynamical Degrees of Freedom: Key critiques argue that the observed entanglement arises from the Newtonian component of the gravitational field, which, in canonical GR, is not associated with the true dynamical gravitational degrees of freedom (i.e., the transverse-traceless or "graviton" modes) but rather from constraint equations slaved to the quantum matter source (Anastopoulos et al., 2018, Fragkos et al., 2022).
Gauge and Locality Ambiguity: The same GIE experiments may be re-expressed in different gauge choices (e.g., Coulomb/Poisson versus Lorentz gauge), leading to equally valid descriptions in terms of local quantum field mediators or instantaneous nonlocal potentials. Hence, observation of entanglement cannot unambiguously distinguish between quantized graviton exchange and gauge-fixed nonlocal interactions (Fragkos et al., 2022).
Classical Gravity-Quantum Matter Theories: In hybrid models such as the DP model, classical gravity coupled to quantum matter yields entanglement through a nonlocal, correlated measurement structure in the master equation. Crucially, GIE is possible in such models, with clear dependences on separation, wavepacket extent, and the model's smearing parameter $\sigma$ , meaning that observation of GIE alone cannot discriminate between quantum and certain classes of classical models (Trillo et al., 4 Nov 2024).
Role of Destructive Interference: The mechanism for entanglement has also been attributed to quantum interference with sign changes and rare-event selection, rather than simply the magnitude of gravitationally induced phases. This has ramifications for optimizing detection signal-to-noise and relaxing experimental constraints (Rostom, 9 Jan 2024).

5. Strategies for Amplification, Detection, and Practical Feasibility

Overcoming the weak gravitational coupling is a recurring challenge, motivating several advancements:

Signal Amplification: Weak-value amplification and two-setting EPR steering are proposed as methods to amplify the observable effects of weak entanglement, distinguishing quantum from classical mediators by logical contradiction in detection statistics (Feng et al., 2022).
State Engineering: Large-spin generalized Stern–Gerlach schemes allow for spatial superpositions over an enlarged phase space; non-maximally entangled or specially tailored spin states are shown to enhance the gravitation-induced entanglement and reduce mass and time thresholds (Braccini et al., 2023).
Relaxed Mass and Control Requirements: Square-well trap schemes show that significant entanglement can be generated at masses well below previously considered "mesoscopic" thresholds, facilitating more accessible tabletop experiments (Zhang et al., 13 Apr 2025).
Cold Atom Ensembles and Squeezing: Entanglement can be realized between cold atomic interferometers operated with classical-like ("coherent") or moderately squeezed atomic states, reducing both the required number of atoms and integration times for feasible signal visibility (Howl et al., 2023).
Time Dynamics and Stability: While DP-type decoherence mechanisms eventually destroy entanglement, the predicted lifetime (on the order of a day for current proposals) provides a significant temporal window for measurement (Trillo et al., 4 Nov 2024). In GW-driven systems, time-crystalline phases and persistent quantum memory effects may be observable (Dutta et al., 25 Mar 2025).

6. Broader Implications and Future Directions

Gravitationally-induced entanglement sits at the nexus of quantum information, experimental quantum optics/mechanics, and foundational gravity research:

Laboratory and Cosmological Cross-Connections: GIE is relevant not only for laboratory probes (e.g., interferometric arrays, optomechanical experiments) but also in curved spacetime and cosmological contexts, where gravitational entanglement and its spectrum may encode information about curvature or cosmic expansion (Brahma et al., 2023, Zhang et al., 2023).
Operational Field-Theoretic Models: The transition towards operational QFT-based models enables direct definition of measurement observables (e.g., center-of-mass projectors constructed from field quadratic forms), providing a rigorous framework for interfacing theory and experiment at weakly relativistic energies (Yant et al., 26 Mar 2025).
Discriminatory Power of GIE Experiments: While the detection of GIE is a landmark in laboratory quantum gravity tests, it is not a definitive signature of quantized gravity. Only more refined protocols—possibly those sensitive to genuine dynamical degrees of freedom (e.g., the graviton’s transverse-traceless polarization) or unequivocal quantum field-theoretic effects—can conclusively distinguish between quantum and classical models (Anastopoulos et al., 2018, Fragkos et al., 2022, Trillo et al., 4 Nov 2024).
Applications Beyond Foundations: Techniques developed to control and observe GIE may find utility in quantum information tasks, sensitive metrology, and quantum communication, wherever ultra-weak nonlocal interactions are involved (Cui et al., 2023, Feng et al., 2022).

The future of GIE research will rely on pushing the frontier of isolation, control, amplification, and measurement in massive quantum systems, while refining theoretical models to account for competing effects and unambiguous tests of the quantization of gravity.