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arXiv:2211.03661 · Physica Scripta

Spatial qubit entanglement witness for quantum natured gravity

Bin Yi, Urbasi Sinha, Dipankar Home, Anupam Mazumdar, Sougato Bose

Published Aug 14, 2026• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1402-4896/ae9a06

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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.
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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.
The paper presents a scheme to detect entanglement arising from the quantum nature of gravity between a spin qubit and photons, using Stokes parameters. One of the crucial tests of the general theory of relativity is the bending of light due to the curvature. Recently, a quantum counterpart of this experiment to test the quantum nature of the gravitational interaction has been proposed, in which the spin-2, massless graviton yields entanglement between matter and a photon sector. Hence, it provides one of the most crucial experimental signatures for testing the quantum nature of gravity in a lab, since only spin-2-induced entanglement can yield the correct deflection of light due to matter. Here, we propose a positive partial-transpose (PPT) witness criterion for witnessing such an entanglement. We scan the entangled states in this context by studying the overlap of the final state, which is proportional to the entanglement phase. We exploit the Stokes observables to measure the photon state and the spins in the matter sector, thereby constructing a witness for the quantum nature of gravity in this setup. To quantify this entanglement, we will couple the photon to a local oscillator, whose phase need to be controlled to probe the orthogonal components of the macroscopic interference in the laser beam. We have shown that for a non-maximally entangled state mediated by the quantum nature of gravity, the witness attains a maximal negativity of −0.052-0.052−0.052. Our findings indicate that this witness effectively detects entanglement within the range 0.71≤∣γ∣<10.71 \leq |γ| < 10.71≤∣γ∣<1, where γγγ is the overlap between the two coherent states of the photon, providing a clear signature of quantum correlations.
The Einstein equivalence principle is based on the equality of gravitational and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities.Here, we provide a simple quantum protocol based on creating large spatial superposition states in a laboratory to test the quantum regime of the equivalence principle where both matter and gravity are treated at par as a quantum entity. The two gravitational masses of the two spatial superpositions source the gravitational potential for each other. We argue that such a quantum protocol is unique with regard to testing especially the generalisation of the weak equivalence principle by constraining the equality of gravitational and inertial mass via witnessing quantum entanglement.