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arXiv:2507.01007 · Scientific Reports

Evolution of tripartite entanglement in three-qubit quantum gravity-induced entanglement of masses (QGEM) with quantum decoherence

Pablo Guillermo Carmona Rufo, Anupam Mazumdar, Carlos Sabín

Published Mar 21, 2026• 0 citations
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Abstract

The recently introduced quantum gravity-induced entanglement of masses (QGEM) protocol aims to test the quantum nature of gravity by witnessing the entanglement produced by the virtual exchange of a graviton between two spatially superposed masses. Shortly after the original proposal, further improvements upon the experiment were suggested, including the addition of a third mass, showing that three-qubit setups can be more resilient to higher rates of decoherence caused by the interaction of the system with the environment. In this work, we investigate the type of tripartite entanglement generated in these three-qubit QGEM experiments when considering the effects of decoherence. We show that the gravitational interaction between the qubits is able to generate genuine tripartite entanglement between them, studying the corresponding parameter spaces and comparing the performance of the possible experimental configurations of the three qubits at allowing for the detection of genuine entanglement via an entanglement witness.

DOI
10.1038/s41598-026-44184-2

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The recently introduced quantum gravity-induced entanglement of masses (QGEM) protocol aims to test the quantum nature of gravity by witnessing the entanglement produced by the virtual exchange of a graviton between two spatially superposed masses. Shortly after the original proposal, further improvements upon the experiment were suggested, including the addition of a third mass, showing that three-qubit setups can be more resilient to higher rates of decoherence caused by the interaction of the system with the environment. In this work, we investigate the type of tripartite entanglement generated in these three-qubit QGEM experiments when considering the effects of decoherence. We show that the gravitational interaction between the qubits is able to generate genuine tripartite entanglement between them, studying the corresponding parameter spaces and comparing the performance of the possible experimental configurations of the three qubits at allowing for the detection of genuine entanglement via an entanglement witness.
Recently, a protocol called quantum-gravity-induced entanglement of masses (QGEM) that aims to test the quantum nature of gravity using the entanglement of two qubits was proposed. The entanglement can arise only if the force between the two spatially superposed masses is occurring via the exchange of a mediating virtual graviton. In this paper we examine a possible improvement of the QGEM setup by introducing a third mass with an embedded qubit so that there are now three qubits to witness the gravitationally generated entanglement. We compare the entanglement generation for different experimental setups with two and three qubits and find that a three-qubit setup where the superpositions are parallel to each other leads to the highest rate of entanglement generation within $\ensuremath{\tau}=5\phantom{\rule{4pt}{0ex}}\mathrm{s}$. We show that the three-qubit setup is more resilient to the higher rate of decoherence. The entanglement can be detected experimentally for the two-qubit setup if the decoherence rate $\ensuremath{\gamma}$ is $\ensuremath{\gamma}<0.11\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$ compared to $\ensuremath{\gamma}<0.16\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$ for the three-qubit setup. However, the introduction of an extra qubit means that more measurements are required to characterize entanglement in an experiment. We conduct experimental simulations and estimate that the three-qubit setup would allow detecting the entanglement in the QGEM protocol at a 99.999.9%99.9 certainty with O(104)−−O(105)O({10}^{4})--O({10}^{5})O(104)−−O(105) measurements when $\ensuremath{\gamma}\ensuremath{\in}[0.1,0.15]\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$. Furthermore, we find that the number of needed measurements can be reduced to O(103)−−O(105)O({10}^{3})--O({10}^{5})O(103)−−O(105) if the measurement schedule is optimized using joint Pauli basis measurements. For $\ensuremath{\gamma}>0.06\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$ the three-qubit setup is favorable compared to the two-qubit setup in terms of the minimum number of measurements needed to characterize the entanglement. Thus, the proposed setup here provides a promising avenue for implementing the QGEM experiment.
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)O({10}^{3})O(103) measurements are required to reject the no-entanglement hypothesis with a parallel-qubit setup without decoherence at a 99.999.9%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)O({10}^{6})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.
In the context of the QGEM (Quantum Gravity-induced Entanglement of Masses) experiment, we consider two adjacent matter-wave interferometers in linear and parallel configurations that interact solely via gravity. If gravity were quantum, then the two matter-wave interferometers would become entangled via the virtual excitation of the massless graviton. In this paper, we consider witnessing this entanglement by considering a generic experimental scenario where the two interferometers are subject to different global phases and different decoherence rates. In this context, we show that the individual global phases do not affect the witness, discuss common and differential decoherence modes, and perform the parameter search optimal for different masses. We provide a mathematical framework for these asymmetric decoherence rates and then search for parameters that determine the entanglement witness. We have kept the inter-separation distance between the two closest superpositions of the interferometers' masses fixed while varying the experimental time from τ=0.1τ=0.1τ=0.1 s to τ=1τ=1τ=1 s. Finishing the experiment at $ τ=0.1$ s has many advantages from the point of view of protecting the experiment from random acceleration noise. However, witnessing the entanglement also suffers from ⟨W⟩∼−O(10−2)\langle W\rangle \sim -{\cal O}(10^{-2})⟨W⟩∼−O(10−2) for m=10−14m=10^{-14}m=10−14~kg, for decoherence rate in the ranges of O(10−1−1){\cal O}(10^{-1}-1)O(10−1−1)~Hz for τ=0.1τ=0.1τ=0.1 s experiment. However, as we show, increasing the mass of the matter-wave interferometer may improve the witness considerably.
We investigate the generation rate of quantum gravity induced entanglement of masses (QGEM) in setups with multiple quantum massive particles, among which only the gravity interaction due to the Newton potential is taken into account. When the distance between any two adjacent Stern-Gerlach devices is fixed, we consider all the possible configurations of the setup with the same number of particles. In particular, we systemically analyze the case of particle number n=4n=4n=4 and find that the prism setup with a massive particle at the center is the most efficient setup for the entanglement generation. This result can be extended to a system with multiple particles up to seven, where the entanglement efficiency is also enhanced in comparison with the setup with fewer particles. This work provides the strategy to construct the quantum gravity induced entanglement of masses setup with the best generation rate of entanglement.
Abstract Witnessing the quantum nature of gravity through the entanglement of two masses has recently been proposed. Both non-Gaussian and Gaussian protocols have been shown to be useful for this purpose. In non-Gaussian protocols the complete 1 / r gravitational interaction can in principle be utilized for entanglement generation, as long as quantum superpositions of a spatial splitting Δ x comparable to the distance d between two masses can be generated. In practice, however, all non-Gaussian protocols proposed to date rely on embedded qubits—typically spins—to read out the entanglement: spin correlations are used to witness the entanglement developed between the masses during interferometry. Here we show that if superpositions of distinct spatially localized states of each mass can be created, then a spinless version of the non-Gaussian protocol is possible: simple position correlation measurements alone can yield a spatial qubit witness of the entanglement between the masses. We find that the principal new requirement for the viability of this protocol is a position squeezing of the wavefunction by approximately seven orders of magnitude, applied at a specific stage of the experiment.
A recently proposed experimental protocol for quantum gravity induced entanglement of masses (QGEM) requires in principle realizable, but still very ambitious, set of parameters in matter-wave interferometry. Motivated by easing the experimental realization, in this paper, we consider the parameter space allowed by a slightly modified experimental design, which mitigates the Casimir potential between two spherical neutral test masses by separating the two macroscopic interferometers by a thin conducting plate. Although this setup will reintroduce a Casimir potential between the conducting plate and the masses, there are several advantages of this design. First, the quantum gravity induced entanglement between the two superposed masses will have no Casimir background. Secondly, the matter-wave interferometry itself will be greatly facilitated by allowing both the mass ${10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}15}\phantom{\rule{0.28em}{0ex}}\mathrm{kg}$ and the superposition size $\mathrm{\ensuremath{\Delta}}x\ensuremath{\sim}20\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ to be a one-two order of magnitude smaller than those proposed earlier, and thereby also two orders of magnitude smaller magnetic field gradient of ${10}^{4}\phantom{\rule{0.28em}{0ex}}{\mathrm{Tm}}^{\ensuremath{-}1}$ to create that superposition through the Stern-Gerlach effect. In this context, we will further investigate the collisional decoherences and decoherence due to vibrational modes of the conducting plate.