Gravitationally induced entanglement between two masses: a registered prediction of no witness below an entangling phase of 2 rad, at any constant recording rate
I register the prediction that no experiment will witness gravitationally induced entanglement between two masses, each in two branches, while their entangling phase stays below 2 rad, at any constant rate at which each mass's environment records its position. Under gravity whose source in each description is a function of the system's reduced state, conditioned on every record that exists, two masses that nothing records stay in a product state at every entangling phase. Recorded masses stay unentangled while the phase is below 4 rad with each mass's share counted once, or below 2 rad with each mass taking its full potential. Every published parameter set computed here lies below both, between 0.0150 rad and 0.594 rad. A witness of gravitationally induced entanglement reported at 5 standard deviations in any such experiment excludes the prediction on its own, whatever the recording rate. Quantized gravity entangles the masses only while each is recorded more slowly than a threshold set by the experiment's parameters, 0.0623 /s at Bose et al.'s, so a null result counts against it only where an experiment establishes its recording rate below that threshold. The source in the description occupying branch A is n_r^A = n_A + f(η) (n_B − n_A)/2, where n_A and n_B are the branches' densities and η is the overlap of the mass's two branch records, e^(−Γ t) at recording rate Γ. The product state is derived; the weight f(η) = η is derived from the stated condition that the source depend affinely on the coherence; the phase bound is computed in a two-branch open-system model and rests on the stated two-body form. Nothing is fitted. The statistic is the reported witness with the recording rate the experiment establishes, read against both predictions at its own parameters; the chance of a false exclusion from statistical fluctuation alone is 2.9 × 10⁻⁷ for each experiment.
I register the prediction that no experiment will witness gravitationally induced entanglement between two masses, each in two branches, while their entangling phase stays below 2 rad, at any constant rate at which each mass's environment records its position. Under gravity whose source in each description is a function of the system's reduced state, conditioned on every record that exists, two masses that nothing records stay in a product state at every entangling phase. Recorded masses stay unentangled while the phase is below 4 rad with each mass's share counted once, or below 2 rad with each mass taking its full potential. Every published parameter set computed here lies below both, between 0.0150 rad and 0.594 rad. A witness of gravitationally induced entanglement reported at 5 standard deviations in any such experiment excludes the prediction on its own, whatever the recording rate. Quantized gravity entangles the masses only while each is recorded more slowly than a threshold set by the experiment's parameters, 0.0623 /s at Bose et al.'s, so a null result counts against it only where an experiment establishes its recording rate below that threshold. The source in the description occupying branch A is n_r^A = n_A + f(η) (n_B − n_A)/2, where n_A and n_B are the branches' densities and η is the overlap of the mass's two branch records, e^(−Γ t) at recording rate Γ. The product state is derived; the weight f(η) = η is derived from the stated condition that the source depend affinely on the coherence; the phase bound is computed in a two-branch open-system model and rests on the stated two-body form. Nothing is fitted. The statistic is the reported witness with the recording rate the experiment establishes, read against both predictions at its own parameters; the chance of a false exclusion from statistical fluctuation alone is 2.9 × 10⁻⁷ for each experiment.
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.
Most proposed table-top tests of gravity in the quantum regime use equal-amplitude spatial superpositions and seek either gravitationally induced entanglement or collapse-motivated loss of interference. This paper develops a complementary theory-classification framework in which branch weights are scanned as operational control parameters. A massive source is prepared in a two-branch state∣ψp⟩=p∣L⟩+1−p∣R⟩,or, more generally, in an m-branch state∣ψ⟩=∑a=1mpaeiθa∣a⟩.The elementary two-branch second cumulant p(1−p)(Δq)2 is treated as a baseline branch-resolution law, not as a quantum-gravity signature. The main object is an enlarged witness geometry combining mean response, branch-induced covariance and higher cumulants, operational recoverability, and excess-noise or irreversibility coordinates. The m-branch extension yields simplex and covariance-rank constraints; the n-particle extension distinguishes independent ensembles from collectively entangled branch states by n versus n2 scaling. Recoverability is formulated as a resource-theoretic witness convention: adaptive recovery may use probe instruments and classical feed-forward but may not introduce an independent branch-basis coherence resource; a separate joint-recovery functional captures coherent erasure using accessible source-probe correlations. Worked models illustrate deterministic expectation-value gravity, coherent branch-mediated interaction, effective irreversible branch-basis dephasing, and noisy classical measurement-feedback dynamics. A finite-record, calibrated measurement-feedback bound shows that, within that simulator class, reproducing nontrivial branch-conditioned response requires record distinguishability; the associated record overlaps bound adaptive recovery of source coherence, with response-calibrated corollaries when the feed-forward range is bounded. The resulting framework is not a new microscopic theory of gravity. It is a model-discrimination scheme for locating gravitational response models in a witness space generated by branch-weight, branch-number, and ensemble-size scans.
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.
Recently, a theoretical and an experimental protocol known as quantum-gravity-induced entanglement of masses (QGEM) has been proposed to test the quantum nature of gravity using two mesoscopic masses, each placed in a superposition of two locations. If after eliminating all nongravitational interactions between them the particles become entangled, one can conclude that the gravitational potential is induced via a quantum mediator, i.e., graviton. In this paper we explore extensions of the QGEM experiment to multidimensional quantum objects and examine a range of different experiment geometries, in order to determine which would generate entanglement faster. We conclude that when a sufficiently high decoherence rate is introduced, multicomponent superpositions can outperform the two-qubit setup. With low decoherence however, and given a maximum distance $\mathrm{\ensuremath{\Delta}}x$ between any two spatial states of a superposition, a set of two qubits placed in spatial superposition parallel to one another will outperform all other models given realistic experimental parameters. This is further verified with an experiment simulation, showing that O(103) measurements are required to reject the no-entanglement hypothesis with a parallel-qubit setup without decoherence at a 99.9 confidence level. The number of measurements increases when decoherence is introduced. When the decoherence rate reaches 0.125 Hz, six-dimensional qudits are required as the two-qubit system entanglement cannot be witnessed anymore. However, in this case, O(106) measurements will be required. One can group the witness operators to measure in order to reduce the number of measurements (up to tenfold). However, this may be challenging to implement experimentally.
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.