We use a quantum variant of the Sagnac interferometer to argue for the quantum nature of gravity assuming the equivalence principle, which we formulate in its quantum version. We first present an original derivation of the phase acquired in the conventional Sagnac matter-wave interferometer, within the Hamiltonian formalism. Then we modify the interferometer in two crucial respects. The interfering matter wave is interfered along two different distances from the centre and the interferometer is prepared in a superposition of two different angular velocities. We argue that if the radial and angular degrees of freedom of the matter wave become entangled through this experiment, then, via the equivalence principle, the gravitational field must be non-classical.

我们使用萨格纳克干涉仪的量子变体来论证引力的量子性质，假设等效原理，我们在其量子版本中公式化。我们首先在哈密顿形式主义中展示了在传统萨格纳克物质波干涉仪中获得的相位的原始推导。然后我们在两个关键方面修改干涉仪。干涉物质波沿距中心的两个不同距离进行干涉，干涉仪准备在两个不同角速度的叠加中。我们认为，如果物质波的径向和角自由度通过这个实验纠缠在一起，那么，根据等效原理，引力场一定是非经典的。