We show that gravitational curvature can control the generation of nonlocal quantum correlations in a hybrid qubit-mechanical device. The tidal field of a nearby source mass modifies the susceptibility of a shared mechanical oscillator, thereby tuning an oscillator-mediated qubit-qubit interaction and the resulting entangling phase. An exact treatment of the dynamics reveals stroboscopic geometric gates whose accumulated phase is directly sensitive to gravitational curvature. Treating the curvature as an unknown parameter, we derive the ultimate quantum limit for its estimation and identify a parity-based measurement that saturates this bound. Solving the full master equation with the mechanical mode retained explicitly, we find that thermal occupation of the mediator suppresses entanglement between the closure times but is undone at each closure, exactly in the unitary limit for any initial mechanical temperature, so that ground-state cooling of the oscillator is not a prerequisite for the protocol. Mechanical damping and qubit dephasing behave differently: they leak branch information irreversibly to the environment, and it is the heating and dephasing rates, rather than the bath occupation alone, that limit the entanglement visibility and the number of usable interrogation loops. In contrast to gravity-mediated entanglement proposals, entanglement is generated by the mechanical oscillator while gravity acts solely as a classical control field. We quantify the achievable curvature parameters; all curvature dependencies are analytic, allowing for exact rescaling of the results. The scheme therefore demonstrates gravitational control of a quantum interaction and provides a route to curvature sensing based on a nonlocal two-qubit phase rather than on local phase measurements.
We show that gravitational curvature can control the generation of nonlocal quantum correlations in a hybrid qubit-mechanical device. The tidal field of a nearby source mass modifies the susceptibility of a shared mechanical oscillator, thereby tuning an oscillator-mediated qubit-qubit interaction and the resulting entangling phase. An exact treatment of the dynamics reveals stroboscopic geometric gates whose accumulated phase is directly sensitive to gravitational curvature. Treating the curvature as an unknown parameter, we derive the ultimate quantum limit for its estimation and identify a parity-based measurement that saturates this bound. Solving the full master equation with the mechanical mode retained explicitly, we find that thermal occupation of the mediator suppresses entanglement between the closure times but is undone at each closure, exactly in the unitary limit for any initial mechanical temperature, so that ground-state cooling of the oscillator is not a prerequisite for the protocol. Mechanical damping and qubit dephasing behave differently: they leak branch information irreversibly to the environment, and it is the heating and dephasing rates, rather than the bath occupation alone, that limit the entanglement visibility and the number of usable interrogation loops. In contrast to gravity-mediated entanglement proposals, entanglement is generated by the mechanical oscillator while gravity acts solely as a classical control field. We quantify the achievable curvature parameters; all curvature dependencies are analytic, allowing for exact rescaling of the results. The scheme therefore demonstrates gravitational control of a quantum interaction and provides a route to curvature sensing based on a nonlocal two-qubit phase rather than on local phase measurements.
This paper establishes a geometric bridge between two operational results concerning gravity-mediated entanglement and phase-based field structure. First, prior work showed that entanglement in minimal gravity-mediated interferometric models arises if and only if the interaction phases contain a non-factorable plaquette invariant. This invariant represents an oriented loop phase that cannot be decomposed into local contributions and therefore serves as a necessary and sufficient condition for entanglement generation. Second, the Harmonic Code framework describes persistent physical effects as loop-structured phase geometry, in which closed phase loops encode enduring information about curvature and field structure. The present work unifies these viewpoints by demonstrating that the plaquette phase emerges naturally as a curvature-induced loop holonomy. An effective phase-gradient field is introduced, and the oriented loop phase is defined as Π = ∮ k · dℓ = ∬ (∇ × k) · dA, showing that the non-factorable phase invariant is directly generated by the curl of the phase-gradient field. A minimal rotational field model is used to derive the relation Π = 2εA, where A is the enclosed area and ε is the curl parameter. Numerical simulations verify the key geometric properties expected of a true holonomy: Linear scaling with enclosed area Shape independence at fixed area Sign reversal under orientation flip Convergence under discretization refinement The loop phase Π is then mapped to standard two-qubit entanglement measures. For the separable input state |++⟩, the concurrence and negativity are shown to depend only on Π: C(Π) = |sin(Π/2)| N(Π) = C/2 These results demonstrate that the non-factorable phase structure required for gravity-mediated entanglement has a direct geometric origin as a curvature-induced loop holonomy. The paper therefore provides a unified operational statement: Curvature generates loop phases, and those loop phases are exactly the structures responsible for gravity-mediated entanglement. This establishes a concrete geometric mechanism linking spacetime curvature, phase holonomy, and quantum entanglement, and offers a clear, experimentally testable framework for probing quantum aspects of gravity.
Gravity-induced entanglement has been proposed as a method for testing the non-classical nature of gravity via tabletop experiments. While most existing proposals are restricted to the Newtonian limit, the frame dragging effect offers access to genuinely post-Newtonian features of the gravitational interaction and remains comparatively less explored. Here, we study gravity-induced entanglement generated by frame dragging in an interferometric setting and compute the entanglement phase between the rotational degrees of freedom of a source mass and the paths of a particle in two complementary ways: (i) via Schrödinger evolution with a quantized Lense-Thirring Hamiltonian in the large angular momentum limit, and (ii) via the on-shell action of linearized quantum gravity within the stationary phase approximation. Both approaches yield the same entanglement phase, consistent with the proper time difference between the interferometer arms. The path integral derivation further reveals how gravitational retardation modifies the entanglement phase, thereby making the local, relativistically causal linearized-gravity description explicit. Under the standard locality/mediator assumptions used in existing arguments, the resulting entanglement would witness non-classicality of the gravitational interaction.
Gravity can both generate quantum entanglement and cause decoherence through time-dilation effects. This note studies the competition between these two effects by treating them as consequences of the same Newtonian mass–energy interaction. Using a solvable two-body model with a coupling between energy and geometry, the work shows that the position-dependent part of the interaction produces the entangling phases associated with gravitationally induced entanglement, while the energy-dependent part produces proper-time decoherence. The paper computes this race exactly and derives several results. First, the outcome is independent of the strength of gravity itself: the dynamics depends only on the combination of coupling strength and interaction time, meaning that gravity sets the timescale but does not determine the final verdict. The result is controlled by the structure of the interaction and the geometry of the quantum state. Second, a registered prediction that internal energy spread would eventually destroy gravitational entanglement is disproved by the exact calculation. Instead, the entanglement decreases but approaches a nonzero geometry-dependent floor. The mechanism is traced to the energy-product coupling, which produces a non-Gaussian characteristic function and prevents complete suppression of the entangling effect. Third, the work derives an exact separability boundary: two sources with spatial coherences v1 and v2 become entangled at the optimal phase precisely when (1 + v1)(1 + v2) > 2. Fully decohered sources cannot generate entanglement, while partial coherence can be sufficient. Finally, the paper verifies that the record–decoherence relation holds inside the same gravitational interaction: coherence lost by a system equals the information recorded by the rest of the universe, combining entanglement and proper-time decoherence into a single information budget. The results are obtained within finite exactly solvable models with declared limitations: static branches, Newtonian-form coupling, no graviton exchange, and no dynamical quantum gravity. The work provides a controlled theoretical framework for understanding the competition between gravitationally induced entanglement and gravitational decoherence.
We investigate gravitationally generated entanglement in two quantum harmonic oscillators induced by quadratic (Stelle) gravity, including corrections up to 1.5 post-Newtonian order. Starting from the quadratic action, we derive the effective two-body Hamiltonian for two harmonically trapped masses, incorporating the contributions of the massive spin-2 ghost (m2) and massive spin-0 (m0) degrees of freedom of the gravitational field. For two quantised oscillators prepared in their ground state, we compute the von Neumann and Rényi entropies of the reduced state and identify a frequency at which the gravitationally-induced entanglement vanishes due to cancellation between relativistic momentum squeezing and quantum-delocalisation-induced position squeezing. We further analyze the cancellation frequency and derive the approximate constraint m0<34m2 for the spin-2 and spin-0 modes. This relation follows from demanding a stable harmonic oscillator description. Finally, we study gravitationally-induced concurrence in a non-Gaussian setup and show how quadratic gravity modifies the entanglement generated between two spatial superpositions. The concurrence can approach O(1) for certain choices of mass, spatial superposition, particle distance, and spin-2 and spin-0 modes. The concurrence will deviate from Newtonian gravity at certain particle separations, depending on the energy of the spin-2 and spin-0 modes. For example, spin modes as low as 0.0197 eV become distinguishable from Newtonian gravity at a distance d∼40μm. This allows us to constrain the spin-2 and spin-0 masses in experiments.
In recent years, the quantum nature of gravity has attracted significant attention as one of the most important problems in modern physics. Here, we analyze the mechanism of gravitationally-induced entanglement from the perspective of quantum resource theory. Building on the framework of Bose et al. [Phys. Rev. Lett. 119, 240401 (2017)], we show that the gravitational interaction acts as a unitary channel, redistributing quantum resources between two spatially superposed masses. Specifically, we demonstrate that the resulting bipartite entanglement originates from the coherent conversion of local quantum coherence -- initially present in each subsystem -- into shared non-local correlations. We derive exact, analytical complementarity relations quantifying this conversion, link the decay of local coherence directly to the growth of entanglement, and support these findings with numerical simulations. Our results clarify the underlying mechanism and establish gravity as a coherence-to-entanglement conversion channel, offering a refined interpretive basis for forthcoming experimental tests. Crucially, we show that initial coherence is a necessary condition for entanglement generation and that its degree bounds the maximum achievable entanglement, with maximal entanglement requiring initial maximal coherence.
This work presents an explicit Newtonian gravitational phase model for two masses placed in spatial superposition and demonstrates that the resulting phase structure produces a non-zero plaquette invariant. Numerical simulations show that the plaquette phase scales with branch separation, generates entanglement according to analytic mappings, and vanishes under loop-removal kill tests. These results provide a fully operational demonstration that Newtonian gravitational phase accumulation produces the non-factorable loop structure required for gravity-mediated entanglement.