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arXiv:2311.08291

Distribution of quantum gravity induced entanglement in many-body systems

Pratik Ghosal, Arkaprabha Ghosal, Somshubhro Bandyopadhyay

Published Nov 14, 2023• 0 citations
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Abstract

Recently, it was shown that if two distant test masses, each in a spatially superposed quantum state, become entangled due to their mutual gravitational interaction, then this entanglement could serve as evidence of the quantum nature of gravity. We extend this treatment to a many-body system in a general setup and study the entanglement properties of the time-evolved state. We exactly compute the time-dependent I-concurrence for every bipartition and obtain the necessary and sufficient condition for the creation of genuine many-body entanglement. We further show that this entanglement is of generalised GHZ type when certain conditions are met. We also evaluate the amount of multipartite entanglement in the system using a set of generalised Meyer-Wallach measures.

DOI
10.48550/arxiv.2311.08291

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Recently, it was shown that if two distant test masses, each in a spatially superposed quantum state, become entangled due to their mutual gravitational interaction, then this entanglement could serve as evidence of the quantum nature of gravity. We extend this treatment to a many-body system in a general setup and study the entanglement properties of the time-evolved state. We exactly compute the time-dependent I-concurrence for every bipartition and obtain the necessary and sufficient condition for the creation of genuine many-body entanglement. We further show that this entanglement is of generalised GHZ type when certain conditions are met. We also evaluate the amount of multipartite entanglement in the system using a set of generalised Meyer-Wallach measures.
Abstract Recently, it was shown that if two distant test masses, each in a spatially superposed quantum state, become entangled due to their mutual gravitational interaction, then this entanglement could serve as evidence of the quantum nature of gravity. We extend this treatment to a many-body system in a general setup and study the entanglement properties of the time-evolved state. We exactly compute the time-dependent I-concurrence for every bipartition and obtain the necessary and sufficient condition for the creation of genuine many-body entanglement. We further show that this entanglement is of generalised GHZ type when certain conditions are met. We also evaluate the amount of multipartite entanglement in the system using a set of generalised Meyer-Wallach measures.
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.
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.
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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.
Abstract One of the outstanding questions in modern physics is how to test whether gravity is classical or quantum in a laboratory. Recently there has been a proposal to test the quantum nature of gravity by creating quantum superpositions of two nearby neutral masses, close enough that the quantum nature of gravity can entangle the two quantum systems, but still sufficiently far away that all other known Standard Model interactions remain negligible. However, preparing superposition states of a neutral mass (the light system) requires the vicinity of laboratory apparatus (the heavy system). We will suppose that such a heavy system can be modelled as another quantum system; since gravity is universal, the lighter system can get entangled with the heavier system, providing an inherent source of gravitational decoherence. In this paper, we will consider a toy model composed of two light and two heavy quantum oscillators prepared in the motional ground state, forming pairs of probe-detector systems, and study under what conditions the entanglement between two light systems evades the decoherence induced by the heavy systems. We conclude by estimating the decoherence in the proposed experiment for testing the quantum nature of gravity.