Gravity-Mediated Entanglement

• Gravity-mediated entanglement is the process by which two quantum systems become entangled exclusively via their gravitational interaction, highlighting the nonclassical nature of gravity.
• Experimental and theoretical protocols, including path superposition, oscillator, and rotational methods, detect phase shifts, squeezing, and relativistic signatures indicative of quantum mediation.
• Practical challenges involve isolating gravitational effects from other forces, mitigating decoherence, and achieving precise control over mass, distance, and coherence time to certify entanglement.

Gravity-mediated entanglement refers to the physical phenomenon in which two quantum systems become entangled exclusively through their mutual gravitational interaction. This effect has become a central focus in the quest to determine whether gravity is a fundamentally quantum field or remains classical even in regimes where all other interactions are demonstrably quantum mechanical. The detection or inference of entanglement generated solely by gravitational interaction is now widely regarded as a model-independent witness of nonclassical features of the gravitational field, motivating a diverse range of proposals, theoretical frameworks, and experimental efforts.

1. Theoretical Foundations: Mediator Quantum-ness and General No-Go Results

A central theorem underlying the field is that any channel (mediator) capable of generating entanglement between two quantum systems must itself possess non-commuting observables, i.e., must be quantum. In the general information-theoretic framework, if systems $A$ and $B$ each interact locally with a third system $C$ (the mediator, e.g., gravity), and subsequently $A$ and $B$ become entangled, then $C$ cannot be a classical system described by a commutative algebra of observables (Marletto et al., 2017, Ludescher et al., 17 Jul 2025). The algebraic structure is formalized by modeling classical systems as commutative unital C*-algebras, possibly infinite-dimensional, thereby encompassing continuous classical fields and general classical mediators. When $C$ is commutative, local operations and classical communication (LOCC), including arbitrary local quantum channels and conditioning, cannot generate entanglement between $A$ and $B$ after tracing out $C$. This result holds regardless of whether $A$, $B$, and $C$ are finite- or infinite-dimensional; in particular, any classical field theory, no matter how complex, cannot function as an entangling channel (Ludescher et al., 17 Jul 2025).

The quantum nature of gravity is thus inferred indirectly: observing gravity-mediated entanglement between quantum systems is mathematically incompatible with any classical (commutative) description of the mediator.

2. Experimental Proposals and Protocol Designs

Most gravity-mediated entanglement ("GME") proposals adopt one of two primary regimes:

• Path Superposition Protocols: Two massive particles are prepared in spatial superpositions (e.g., Mach–Zehnder or Stern–Gerlach interferometers) such that each can take one of two or more distinct paths. The gravitational interaction, dependent on the path combination, imprints relative phases on each branch of the composite state. After evolution and recombination, an analysis of the final state—probabilities, spin correlations, or interference—can witness entanglement. The canonical entangling phase is given by

$\phi_{ij} = \frac{G m^2}{\hbar d_{ij}} \Delta t$

where $d_{ij}$ is the distance between the masses in branches $i$, $j$, and $\Delta t$ is the interaction time (Marletto et al., 2017, Bose et al., 2017, Bengyat et al., 2023).

• Continuous-Variable or Oscillator Protocols: Two harmonic oscillators (mechanically trapped or released) interact gravitationally, and their quantum states are monitored. The quadratic (second-order Taylor) term in the Newtonian potential $V(r) \approx (G m^2 / L^3) r^2$ acts as a two-mode squeezing interaction, generating entanglement between their respective positions and momenta. The relevant entanglement measures include logarithmic negativity and entropy, with experimental observables tied to covariance matrix elements (Krisnanda et al., 2019, Kumar, 12 May 2024).
• Relativistic Rotational Protocols: Proposals using superpositions of internal (rotational) energies produce a controlled phase via gravitational mass–energy equivalence. The entangling phase generated between two particles prepared in a superposition of rotational energies $E$ and separated by $r$ is

$\phi = \frac{G E^2 T}{\hbar c^4 r}$

highlighting that the protocol's effect disappears in the classical ($c\to\infty$) limit and thus probes a uniquely relativistic gravitational signature (Higgins et al., 4 Mar 2024).

Table: Regimes and Key Features

Protocol Type	Physical Mechanism	Observable Signature
Path Superposition	Branch-dependent phase	Fringe shift, spin witness
Continuous-Variable	Two-mode squeezing	Negativity/log entropy
Rotational Superposition	Mass–energy coupling	Relativistic entanglement

3. Mathematical Structure and Role of the Mediator

In all gravity-mediated entanglement scenarios, the mathematical crux is the capacity of the mediator to encode superpositions and coherence. Within the path-integral or operator formalism, the gravitational field is sourced by superposed mass configurations (or energy, in the relativistic protocol). The joint quantum state is

$$|\Psi(t)\rangle = \sum_{i,j} c_{ij} |i\rangle_A |j\rangle_B |g_{ij}(t)\rangle$$

with $|g_{ij}(t)\rangle$ representing classical (but branch-dependent) gravitational field states (Bengyat et al., 2023). This construction means that for entanglement to appear, the gravitational field must itself remain in a superposition of distinct configurations correlated with the matter branches. If the field's coherence (the off-diagonal elements in the $|g_{ij}\rangle\langle g_{kl}|$ basis) is destroyed by measurement or decoherence (e.g., radiative processes or environmental noise), the entanglement between $A$ and $B$ is lost.

The generalization to infinite-dimensional mediators demonstrates that only noncommutative mediators (i.e., truly quantum fields) are able to facilitate such joint, coherent evolutions (Ludescher et al., 17 Jul 2025).

4. Retardation, Lorentz Invariance, and Causal Structure

A robust feature of modern theoretical analyses is explicit treatment of Lorentz invariance and causality. Using the path-integral formalism and linearized general relativity, gravitationally-induced phases are shown to accumulate only at timelike and lightlike separations (encoded via retarded Green's functions),

$c[t-t_{ab}] = |x_B(t) - x_A(t_{ab})|$

where $t_{ab}$ is the retarded time (Christodoulou et al., 2022). This formalism demonstrates that experiments can be designed (conceptually, if not technologically) to probe the difference between instantaneous (Newtonian) and causally-propagating (relativistic) gravitational interactions: "retarded entanglement" can only appear after the light-crossing time between masses, which cannot be mimicked by a truly classical instantaneous potential.

These analyses open the avenue for distinguishing between semirelativistic "quantum-controlled classical field" models and fully quantized fields, particularly when interaction times become comparable to or shorter than the light-crossing time.

5. Experimental Challenges, Decoherence, and Metrological Constraints

The extreme weakness of gravity (Planck scale suppression) renders the detection of gravity-mediated entanglement technologically demanding. Key experimental challenges include:

• Isolating the systems from non-gravitational interactions (e.g., electromagnetic, Casimir, and van der Waals forces).
• Suppressing environmental decoherence sources (thermal, collisional, blackbody photons) to maintain quantum coherence and enable measurable phase accumulation (Marletto et al., 2017, Krisnanda et al., 2019).
• Achieving the required mass, spatial separation, and coherence time such that the accumulated phase and resulting entanglement can be certified above statistical and technical noise (Kumar, 12 May 2024).
• For rotational energy protocols, producing macroscopic rotors with precisely controlled and long-lived rotational superpositions at the required energy scale—challenging due to the $1/c^4$ suppression in the relativistic phase (Higgins et al., 4 Mar 2024).
• In protocols using squeezed light or optomechanics, matching the mechanical frequencies and minimizing mechanical–optical entanglement "leakage" is essential. Modulation of the optomechanical coupling can dramatically accelerate entanglement generation ($\sim t^3$ scaling) but augments decoherence at the same rate. There exists a fundamental bound on the product of mechanical relaxation rate and temperature, $\gamma_R k_B T \lesssim (\hbar G m)/(2d^3)$, that cannot be circumvented by control protocols (Plato et al., 2022).

6. Interpretational Subtleties and Alternative Mediators

There are significant subtleties in interpreting observed entanglement as conclusive evidence for quantum gravity:

• Event-locality vs. System-locality: While all well-designed experiments obey Einstein causality ("event locality"), the consequences for system-local mediation may depend on further assumptions about the implementation of the entangling channel (Martín-Martínez et al., 2022).
• Classical Time Evolution: Approximating the gravitational potential to quadratic order and evolving the system according to Newton's classical laws (via Liouville dynamics or Wigner function evolution) yields identical purity/entanglement predictions as quantum evolution, provided the initial states are nonclassical. Only in regimes sensitive to higher-order terms or genuinely quantum signatures (beyond the second-order) does observation of entanglement unambiguously require quantum gravity (Marchese et al., 15 Jan 2024).
• Quantum Information Approach: Using quantum channels, Choi matrices, and the positive partial transpose (PPT) criterion, experiments verifying the Schrödinger equation for a single delocalized mass with external gravitational sources suffice to demonstrate that two such systems, each in a spatial superposition, must evolve into an entangled state under gravity, provided the time evolution is positive (or completely positive). Therefore, currently feasible matter-wave experiments may already indirectly verify the quantum essence of gravity (Plávala, 5 Aug 2025).

7. Extensions and Generalizations

Gravity-mediated entanglement protocols have been extended or analogized in several directions:

• Photonic implementations: Proposals to witness gravitational entanglement between light beams naturally avoid unwanted massive particle interactions, making the system easier to isolate, though requiring enormous photon number ($N \sim 10^{24}$ at PW powers) to accumulate a measurable gravitational phase. Statistical accumulation, Bell-test violation, and path–entanglement techniques are pivotal (Aimet et al., 2022, Polino et al., 2022).
• Electromagnetic Analogy: Using magnetic-dipole coupling between electron and nuclear spins in a single ion, one can simulate GME in controlled quantum systems. Such analogs clarify that only experiments sensitive to retardation (interaction times on the order of the light-crossing time) test the full quantum field-theoretic character of the mediator (Bian et al., 2023).
• Probing New Physics: Entanglement-witness based protocols have been designed to detect new Yukawa-type interactions, such as those mediated by axion-like particles (ALPs), in addition to modifications of gravity at short distances. The entanglement phase is sensitive to deviations from the Newtonian form, and measurement of entanglement can thus be used to constrain such couplings beyond the Standard Model (Rufo et al., 24 Mar 2025).
• Curved Spacetimes: In cosmological scenarios, entanglement generated via gravitational interactions between oscillators in an expanding universe can, in principle, be used to probe the underlying spacetime curvature, namely, the local expansion rate $H$ (Brahma et al., 2023).

Conclusion

The paper of gravity-mediated entanglement provides a rigorous, quantum information-based route for probing the quantum (versus classical) nature of gravity. Observation of such entanglement is operationally accessible, model-independent evidence that the gravitational field possesses noncommuting observables, a haLLMark of quantum theory. Current and near-future experimental systems—using matter-wave interferometry, optomechanics, spin systems, and photonic circuits—are poised to test these fundamental principles. The precise theoretical and mathematical framework, extending to infinite-dimensional classical field mediators, ensures that only a genuinely nonclassical (quantum) gravity theory can account for the appearance of entanglement generated solely by the gravitational interaction. This result has deep implications for quantum gravity, foundational physics, and experimental quantum information science.