Gravitationally Induced Entanglement of Matter in Quadratic Curvature Gravity and Constraints on Ghost Mass
Abstract
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 < √[3]4 m2 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 ∼ 40 μm. This allows us to constrain the spin-$2$ and spin-$0$ masses in experiments.
Related
- Testing Gravitationally-Induced-Entanglement with Massive Particles and Quantum Clocks
- Optimal Interferometer Geometry for Gravitationally Induced Quantum Entanglement
- Enhancement of Gravitationally Induced Entanglement via Quantum Squeezing
- Gravitationally Induced Entanglement Across an Event Horizon
- Improving Gravitationally Induced Entanglement in Interferometric Configurations
BibTeX
@misc{manen2026gravitationally,
title = {{Gravitationally Induced Entanglement of Matter in Quadratic Curvature Gravity and Constraints on Ghost Mass}},
author = {Linda M. van Manen and Tim Blankenstein and Anupam Mazumdar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22501},
eprint = {2609.22501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22501},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravitationally Induced Entanglement of Matter in Quadratic Curvature Gravity and Constraints on Ghost Mass
AU - Linda M. van Manen
AU - Tim Blankenstein
AU - Anupam Mazumdar
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22501
UR - https://arxiv.org/abs/2609.22501
AB - 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 (m_2) and massive spin-$0$ (m_0) 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 m_0 < √[3]4 m_2 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 ∼ 40 μm. This allows us to constrain the spin-$2$ and spin-$0$ masses in experiments.
ER -