Genuine tripartite entanglement in graviton-matter interactions

We demonstrate the existence of genuine tripartite non-Gaussian entanglement in a quantum gravitational system formed by a quantum harmonic oscillator coupled to a single frequency of a quantized gravitational wave. For this purpose, we introduce a new entanglement witness, well-suited for the graviton-matter interaction Hamiltonian analysed here. We show that the witness is non-zero for the three-mode states generated by the Hamiltonian when the system starts in the ground state, thus proving the generation of genuine multipartite quantum entanglement at the most fundamental level of theoretical graviton-matter interactions.