Results and Discussions Combined with the principle and scheme of quantum lighting, by modeling the ranging task as a multi-target hypothesis testing problem, the limitation of binary hypothesis testing in quantum lighting is broken (Fig. 2). The asymptotic performance of the classical ranging scheme and the entangled ranging scheme is discussed and analyzed, and simulations are carried out. The entanglement upper limit (dotted line) proves the advantages of entangled ranging, as well as the scale advantage in the error index, while the progressive performance (dotted solid line) further demonstrates the advantages of entangled ranging. The error index of the QCB simulation results ( dotted solid line in the entangled case and dotted dashed line in the classical case) shows a 6 dB (4-fold) advantage brought by entanglement, which is consistent with the theoretical analysis (Fig. 3). The relationship between the error probability measurement performance of different ranging schemes and the distance accuracy and target reflectivity is simulated and analyzed. When the target reflectivity is constant, there is an inverse relationship between the error probability performance of the entangled ranging scheme and the ranging accuracy. When the error probability is high, the ranging accuracy is low, and when the error probability is low, the ranging accuracy is high. Besides, the solution proposed in this paper is better than the classical ranging solution in terms of ranging accuracy.

Since the birth of navigation, it has had a huge impact on human life. At present, various navigation and positioning methods based on physical foundations such as sound, light, electricity, magnetism, and force have emerged one after another. Among them, the systems based on radio navigation technology for navigation and detection are the most common, radio navigation is still the main means used in the field of military and civil aviation navigation. Navigation is the process of guiding the safe navigation of the operating body. The main tasks include ranging, angle measurement and positioning, etc. These tasks are premised on obtaining the required navigation parameters. The navigation parameters are mainly divided into four types, namely position, angle, distance and speed. The position is a space-time parameter, including the time and space information of the running body. With the progress of the times and the growth of human needs, although the traditional navigation detection method is still the mainstream application in related fields, the detection accuracy is limited. Besides, it is easy to be interfered, the long-distance weak signal detection ability is not strong, and the safety performance cannot be effectively guaranteed. It has become increasingly prominent that traditional radio navigation methods will gradually fail to meet human needs for navigation. It is of great significance to study new navigation ranging solutions combined with quantum lighting to solve the above problems. Meanwhile, quantum illumination can only interrogate the presence of a target in one polarization-azimuth-elevation-range-Doppler-resolution area array at a time. It sends a signal to a narrow area and judges the presence of a target moving at a fixed speed at a fixed time, while practical navigation systems usually estimate the target's polarization properties, azimuth and elevation, distance and velocity (via Doppler effect). Therefore, it is of great significance to study new solutions to solve this problem and give full play to its advantages.

In this paper, combined with the method and principle of quantum lighting, the cavity electro-optical force converter is used to solve the problem of signal detection, and the energy and quantum state transfer between light waves and microwaves are realized, so that the advantages of the two complement each other. The model is transformed into a multi-objective hypothesis testing problem, and the advantages of the proposed scheme are verified by simulating the target identification error probability index and ranging accuracy of the classical ranging scheme and the proposed scheme.

In this paper, by modeling the ranging task as a multi-target hypothesis testing problem, a quantum entanglement-based navigation ranging scheme is proposed. The principle and model of the ranging scheme are expounded, and the progressive performance of the classical ranging scheme and entanglement measuring scheme is analyzed. On this basis, a quantitative analysis of the common parameters of different ranging schemes is carried out, the ranging performance is compared, and the relationship between ranging accuracy and ranging error probability is analyzed. The proposed scheme outperforms the classical scheme, providing a 6 dB advantage in determining the error exponent for any number of possible ranges. In addition, this ranging scheme can also be used to realize entanglement-assisted communication of pulse position modulation, and provides an application direction for quantum ranging radar with quantum advantages.