Abstract
Microwaves exhibit superior performance in free-space transmission compared to optical waves, primarily due to their ability to penetrate fog and experience lower losses in the Earth's atmosphere. Based on microwave-optical entanglement prepared by nano-cavity electro-opto-mechanic converters, we propose a scheme of a quantum positioning system using the distance-based positioning method. Principles of microwave-optical entanglement preparation and our QPS scheme are introduced in detail. The entanglement feature, system stability and positioning feature of the scheme are analyzed after simulations. Furthermore, we delve into the impact of key parameters, such as transmissivity and photon conversion efficiency, on positioning. Notably, the entanglement degrees for both microwave-optic entanglement at the transmitter and optic-optic entanglement at the receiver surpass one, affirming the efficiency of the scheme in preparing and maintaining entanglement. When transmissivity in beam-splitter models of both ground stations equals 0.5, our scheme achieves a minimal positioning error of 6.4×10-7m2 under ideal conditions. Additionally, we map out traces of a plane through continuous positioning using our scheme. These results demonstrate the theoretical efficiency and robustness of our proposed approach.