This paper points out the importance of the quantum nature of the gravitational interaction with matter in a linearized theory of quantum gravity induced entanglement of masses (QGEM). We will show how the quantum interaction entangles the steady states of a closed system (eigenstates) of two test masses placed in the harmonic traps, and how such a quantum matter-matter interaction emerges from an underlying quantum gravitational field. We will rely upon quantum perturbation theory highlighting the critical assumptions for generating a quantum matter-matter interaction and showing that a classical gravitational field does not render such an entanglement. We will consider two distinct examples; one where the two harmonic oscillators are static and the other where the harmonic oscillators are non-static. In both the cases it is the quantum nature of the gravitons interacting with the harmonic oscillators that are responsible for creating an entangled state with the ground and the excited states of harmonic oscillators as the Schmidt basis. We will compute the concurrence as a criterion for the above entanglement and highlight the role of the spin-2 nature of the graviton for entangling the two harmonic oscillators.
Spatial Qubit Entanglement Witness for Quantum Natured Gravity
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学前沿科学技术研究院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（电子科技大学量子与光子态信息技术教育部重点实验室）；Department of Physics and Astronomy, University College London（伦敦大学学院物理与天文系）；Raman Research Institute（拉曼研究所）；Department of Physics and Astronomy, University of Calgary（卡尔加里大学物理与天文系）；Center for Astroparticle Physics and Space Science (CAPSS), Bose Institute（玻色研究所亚原子粒子物理与空间科学中心）；University of Groningen（格罗宁根大学）；Van Swinderen Institute, University of Groningen（格罗宁根大学范斯温德伦研究所）
When does entanglement through gravity imply gravitons?
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences（维也纳量子光学与量子信息研究所（奥地利科学院））；Nordita, KTH Royal Institute of Technology and Stockholm University（北欧理论天体物理中心，瑞典皇家理工学院和斯德哥尔摩大学）
Graviton-mediated entanglement due to light bending from a quantum rotor
University College London（伦敦大学学院）；Van Swinderen Institute, University of Groningen（格罗宁根大学范斯温德伦研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）
University of Barcelona（巴塞罗那大学）；Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；INAF- Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；ICREA（加泰罗尼亚高级研究学院）
A Bell experiment during inflation: probing quantum entanglement in tensor fluctuations through correlations of primordial scalar curvature perturbations
University of Barcelona（巴塞罗那大学）；Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；INAF- Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；ICREA（加泰罗尼亚高级研究院）
Gravitationally mediated entanglement of fermionic qubits: from static to dynamical limits
Isfahan University of Technology（伊斯法罕理工大学）；Dipartimento di Fisica e Astronomia “Galileo Galilei” Università di Padova（帕多瓦大学伽利略·伽利莱物理与天文学系）；Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院吴健中量子中心）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；INAF - Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；Gran Sasso Science Institute（格兰萨索科学研究所）
