Gravitationally Induced Entanglement

• Gravitationally Induced Entanglement (GIE) is the generation of entanglement between quantum systems solely via gravitational interactions.
• Theoretical models and experimental protocols use phase differences, concurrence, and decoherence metrics to probe GIE in controlled setups.
• GIE research challenges classical gravity frameworks and informs advanced quantum gravity theories through enhanced measurement sensitivity and design protocols.

Gravitationally Induced Entanglement (GIE) refers to the entanglement generated between two spatially separated quantum systems mediated solely via gravitational interaction. GIE is at the core of current experimental and theoretical efforts aiming to probe whether gravity itself must be quantum, by using quantum information principles, entanglement witnesses, and precise laboratory platforms. The existence, measurement, and interpretation of GIE have become focal points in quantum gravity research, spurring a diverse array of proposals, foundational theorems, counterexamples, and experimental designs.

1. Foundational Principles and Mechanisms

In paradigmatic GIE protocols, two neutral masses, typically in the $10^{-15}$–$10^{-13}$ kg regime, are prepared in spatial quantum superpositions by interferometric or spin-dependent methods. The mutual gravitational interaction in the nonrelativistic, Newtonian limit is

$H_{\text{int}} = -\frac{G m_1 m_2}{|x_1 - x_2|}~,$

where each mass's center-of-mass wavefunction is in a superposition of well-separated locations. The time evolution of the two-mass quantum state, projected into the four-branch logical basis $\{|LL\rangle, |LR\rangle, |RL\rangle, |RR\rangle\}$, is diagonal and encodes interaction phases

$$U = \exp\left[- \frac{i}{\hbar} H_{\text{int}} t\right] = \mathrm{diag}(e^{-i\phi_{LL}}, e^{-i\phi_{LR}}, e^{-i\phi_{RL}}, e^{-i\phi_{RR}})$$

with $\phi_{ij} = \frac{G m_1 m_2 t}{\hbar d_{ij}}$, $d_{ij}$ the separation for each branch (Biagio, 4 Nov 2025).

If each mass is initialized in an even superposition $|+\rangle = (|L\rangle + |R\rangle)/\sqrt{2}$, the resulting joint state after gravitational interaction exhibits nonzero concurrence and logarithmic negativity when the relative phase difference

$\delta\phi = \phi_{LR} - \phi_{LL}$

is sufficiently large. For current parameter regimes ($m \sim 10^{-14}$ kg, $\Delta x \sim 100\ \mu$m, $d\sim 200$–$500\ \mu$m, $t\sim 0.1$–$1$ s), concurrence $C \sim |\sin\delta\phi|$ and $C \sim 0.01$–$0.1$ are reachable (Biagio, 4 Nov 2025, Howl et al., 2023).

Theoretically, GIE is predicted both by linearized quantum gravity (where the gravitational field operator has non-commuting observables), and by a class of classical gravity models that violate the so-called “circuit-locality” mediation present in LOCC-type no-go theorems, as discussed below.

2. No-Go Theorems, Classical Models, and Mediation Structure

Standard no-go results in quantum information theory state that Local Operations and Classical Communication (LOCC) cannot generate entanglement between two quantum systems. Models assuming a factorized state space $$\mathcal{H}_A \otimes \mathcal{H}_G \otimes \mathcal{H}_B$$, circuit-local mediation (i.e., only $A$ and $G$, or $B$ and $G$ can directly interact at any time, not $A$ and $B$ simultaneously), and classical gravity ($G$ with commuting observables), yield no possibility of entanglement generation (Biagio, 4 Nov 2025, Schneider et al., 24 Nov 2025).

However, the Newtonian gravitational interaction $H_{\text{int}}$ directly couples $x_1$ and $x_2$—it violates mediation locality. Once this is relaxed, even a classical gravitational field (in the sense of classical potential, but with quantum matter) generates entanglement purely by the structure of the Hamiltonian (Biagio, 4 Nov 2025). This includes models such as Newtonian gravity, Wheeler–Feynman action-at-a-distance theories, and the Diósi-Penrose (DP) collapse model (Trillo et al., 4 Nov 2024). In the DP theory, the quantum state of matter couples to a classical Newton potential derived from continuous measurements of a Gaussian-smeared mass density. The resulting master equation induces both nonlocal unitary evolution (feedback of the classical field) and spatial decoherence, which together can entangle two spatially separated masses if the separation is below a critical $d_c$ proportional to the smearing length $\sigma$: $$d_c \approx 0.85\,\sigma~\text{(horizontal)},\qquad d_c \approx 2.21\,\sigma~\text{(transversal)}~.$$ The resulting entanglement decays on a timescale $\sim 10^5$–$10^6$ s, with no persistent oscillations as in quantum gravity (Trillo et al., 4 Nov 2024). Thus, a mere observation of GIE cannot alone confirm quantum gravity; discrimination requires comparison of entanglement phase, growth rates, and criticality with those of “semiclassical” alternatives.

3. Experimental Systems, Parameter Regimes, and Observables

Experiments to witness GIE span a diverse array of platforms: optomechanical cavities with levitated mirrors, atomic fountain interferometers, solid-state spin labels, and even space-based mg-scale laser interferometers (Miki et al., 28 May 2024, Matsumoto et al., 17 Jul 2025, Howl et al., 2023).

Optomechanical and Space-based Systems

Proposals for optomechanical mirrors on the 0.1–10 g scale, closely spaced ($L \sim$ mm), cooled to below 2 K and tracked by high-sensitivity cavity readout, can in principle reach logarithmic negativity $E_N > 0$ with integration times of several weeks. Critical is the suppression of thermal noise, gas damping, and cosmic-ray scattering to achieve a total decoherence rate

$$\Gamma_{\text{tot}} T_{\text{env}}/(2\pi) \lesssim 10^{-18}~\text{Hz}\cdot\text{K}$$

(Matsumoto et al., 17 Jul 2025). Feedback control and Kalman filtering can further accelerate the onset of GIE and suppress variance, while the use of squeezed input light in optical probing can reduce measurement time by an order of magnitude (Hatakeyama et al., 2 Aug 2025).

Cold Atoms and Coherent State Protocols

Cold-atom interferometers, using coherent (rather than N00N or cat) states, can, in principle, reach necessary mass scales of $M_{\text{tot}} \sim 0.1\, M_P$ and enable GIE measurement via number-difference correlations, with detection accelerated by quantum squeezing (Howl et al., 2023). Spin-squeezing by 20 dB can lower needed particle number or interaction time by factors of $100$.

Exponential Enhancement and Hybrid Protocols

Dynamical protocols using Gaussian unitary operations (trap switching, squeezing), such as exponential expansion of small superpositions, yield exponential increases in GIE observability for given gravitational coupling or mass (Braccini et al., 21 Aug 2024, Cui et al., 2023). For instance, the effective GIE negativity in such protocols obeys $\mathcal{N} \propto g_G\exp(\omega t_-)$, enabling entanglement at greater distances or with reduced mass.

4. Theoretical Interpretations, Model Dependencies, and Ambiguities

At the quantum level, the standard logic is that any physical field mediating entanglement between two quantum systems must itself possess at least two non-commuting observables, i.e., must be non-classical or quantum (Marletto et al., 2017). However, detailed field-theoretic analyses show ambiguities:

• In relativistic quantum field theory (QFT), equivalent predictions for GIE can be obtained whether one works in a local, mediator-based picture (Lorentz gauge), a nonlocal picture (Coulomb/Poisson gauge), or even action-at-a-distance formulations (Wheeler–Feynman), due to path-integral duality and nonlocal constraints (Fragkos et al., 2022, Biagio, 4 Nov 2025). Causality is preserved in all formulations. No experiment distinguishes these QFT pictures even in QED.
• Subsystem independence and strictly factorized Hilbert spaces are not fully realized for gravitationally dressed degrees of freedom due to non-commuting, nonlocal gravitational dressing. Algebraic QFT analyses demonstrate that spacelike commutativity fails for any relationally-dressed observable, so LOCC-type arguments are strictly valid only in approximate, effective models (Boulle et al., 18 Dec 2025).
• Observing GIE rules out all strictly classical field models that enforce mediation locality and commutative observables, but does not suffice to confirm graviton quantization without further assumptions on locality and subsystem independence.

5. Advanced Protocols: Amplification, SNR Optimization, and Geometry

For realistic protocols, the smallness of the gravitational coupling requires sensitivity enhancement:

• Weak value amplification, in combination with EPR steering, can boost a vanishingly small GIE signature by arbitrary factors, enabling observation even with picogram masses and subsecond interaction times. Violations of a classical separable bound on steering visibility provide a decisive signature (Feng et al., 2022).
• Optimization of oscillator geometry, specifically by maximizing a system-specific “form factor” $\Lambda$ (the normalized gravitational tidal coupling between oscillators), can relax environmental and frequency requirements. The theoretical supremum, $\Lambda = 2\pi$, is attained by a “meshed-comb” geometry and can improve permissible noise and temperature bounds by an order of magnitude compared to spherical geometry (Tang et al., 19 Nov 2024).
• Destructive interference, nonmaximal entanglement, and postselection strategies can boost signal-to-noise ratio with relaxed mass, time, or separation constraints, thus facilitating feasible GIE detection in next-generation platforms (Rostom, 9 Jan 2024).

6. Extensions: Quantum Walks, Thermal Effects, and Spacetime Curvature

Quantum-walk-based models with Newtonian gravity as the only interaction channel demonstrate explicit buildup of entanglement between two noninteracting particles, with mass and step-number dependence matching expectations from two-qubit GIE protocols (Badhani et al., 2019).

In more complex settings, thermal effects catalyze and enhance entanglement signatures induced by classical gravitational interactions, such as gravitational waves, and introduce memory-driven, prethermal time-crystalline phases (Dutta et al., 25 Mar 2025). In curved FLRW backgrounds, GIE generation is sensitive to spacetime curvature through graviton mode squeezing, motivating new astrometric and cosmological probes of GIE (Brahma et al., 2023).

7. Open Questions, Experimental Discrimination, and Future Prospects

Although detection of GIE will signal a non-classical channel in gravitational interaction, its precise theoretical implications depend on discrimination between quantum gravity, semiclassical, and hybrid classical–quantum models:

• The Diósi-Penrose model predicts GIE with critical distance $d_c$ and an overdamped, monotonic rise-and-fall of entanglement, in contrast to persistent oscillations in linearized quantum gravity (Trillo et al., 4 Nov 2024).
• Comparative measurement of entanglement growth rate, phase, and distance scaling against theoretical predictions is essential (Biagio, 4 Nov 2025).
• Subsystem (in)dependence and microcausality violations, although negligible for current experiments, present both interpretational nuances and potentially new experimental targets (e.g. bounding the size of spacelike commutators for dressed gravitational observables) (Boulle et al., 18 Dec 2025).
• Further optimization of geometry, readout protocols, squeezing, and quantum control are under active investigation as experiments push toward the required parameter regimes (Tang et al., 19 Nov 2024, Hatakeyama et al., 2 Aug 2025).

In sum, the GIE paradigm remains central to the intersection of quantum information and gravity. The ongoing development of protocol enhancements, model discrimination strategies, and experimental techniques will determine whether tableside GIE tests can provide unambiguous evidence of the quantum nature of gravity or, at a minimum, exclude significant classes of alternative gravitational theories.