As the basic technology for positioning and navigation of unknown targets, ranging technology is closely related to people's life, national defense construction, aerospace exploration, and other aspects. The traditional positioning system can realize navigation ranging by continuously transmitting electromagnetic pulses into space, and the pulses will be reflected to the receiver as the presence of targets. As a result, we can detect the echo pulse and estimate its time delay through the propagation time. Wider bandwidth and greater transmission power of a transmitted electromagnetic pulse signal indicate higher precision of time accuracy. However, due to the restriction of the energy and bandwidth of the electromagnetic pulse, the accuracy of navigation ranging has certain limits. To go beyond the limits of energy, bandwidth, and accuracy in classical measurement, quantum ranging makes use of the entangled state, squeezed state, as well as other characteristics to make the transmitted quantum information have a strong correlation and high density. It can obtain much higher ranging accuracy (Heisenberg limit) than that of classical radio ranging systems, and thus it can be further applied to systems such as navigation, positioning, and gravitational wave measurement. In view of the problem that many previous ranging schemes are highly sensitive to photon loss and that it is difficult to achieve long-distance transmission through quantum interferometry, we use the squeezed state to improve the peak estimation of the time delay and propose a non-classical navigation ranging scheme based on quantum illumination, which makes a statistical judgment on the echo signal of a target to determine the distance parameter. We hope that our study can be helpful for the application of quantum information and the design of future navigation and positioning systems.

The quantum ranging scheme enhanced by Gaussian entanglement can be used for high-precision navigation ranging, whose form is similar to that of the classical radio ranging method. With the ranging scheme based on quantum illumination, a pair of entangled photons is generated through parametric down-conversion, and one photon is emitted as the detection signal, while the other photon is left in the local area as the idle signal. If there is a target, the photon scattered by the target can be entangled with the local photon for entanglement measurement, and additional performance gain can be obtained. In our work, first, the basic principles of radar ranging and quantum illumination are introduced, and the discrimination theory of Gaussian states is deduced. Then, upon the analysis of the statistical properties of three Gaussian states, namely, the coherent state, thermal state, and squeezed state, the new ranging method that uses the quantum squeezing effect to improve the estimation accuracy of the time delay is described, and the proposed quantum illumination scheme is further used to improve the entanglement ranging performance. Finally, given the navigation ranging scheme based on quantum illumination, the performance of the coherent state is compared with that of the two-mode squeezed vacuum (TMSV) state in the application of entanglement ranging. In addition, the Chernoff bound of quantum signal detection is used for quantitative analysis.

The results show that the detection error probability of the TMSV state is about 6 dB lower than that of the coherent state in the exponential part after the idle signal is stored, which effectively improves the performance of the navigation ranging system. The Chernoff bound of the detection error probability decreases as the number of signal photons grows and increases as the number of noise photons rises (Fig. 7). At the same time, the entanglement gain performance of the TMSV state is significantly better than that of the coherent state. According to the analysis of quantum hypothesis theory, the detection performance of navigation ranging based on quantum illumination can be improved by about four times (6 dB) in the exponential part compared with that of the traditional scheme when the number of signal photons is small, or the number of noise photons is large. This gain is significant under the circumstance of low-brightness illumination sources or strong noise environments (Fig. 8). The entangled navigation ranging scheme significantly enhances the signal detection performance, improves the range resolution, and can more sensitively determine the range element with lower error probability, thus realizing high-precision navigation ranging. Compared with the situation of the classical navigation ranging scheme, when the detection probability of the echo pulse signal is the same, the receiver in the squeezed-state quantum illumination ranging scheme will have a lower detection threshold, which will expand the maximum range of the navigation ranging system according to the radar range equation. If the detection threshold D₀ is reduced to 1/16 of the original value, doubling the navigation range is promising.

In this work, a new navigation ranging method based on quantum illumination is proposed. For quantum navigation ranging, we can use the squeezed state and entangled state of the quantum to improve the performance of time delay estimation. Comprehensively utilizing the quantum squeezing and entanglement properties, we focus on the comparison of the entanglement ranging performance between TMSV state and coherent state and the analysis of the quantum Chernoff bound for error probability. When the idle signal is stored at the receiver for entanglement measurement, the detection error probability of the TMSV state decreases by about 6 dB in the exponential part compared with that of the coherent state, which effectively improves the detection performance of the navigation ranging system. The quantum illumination scheme has a higher detection probability when the measurement range is fixed, and meanwhile, the scheme has a larger measurement range when the detection probability is the same as that of the classical ranging scheme. Therefore, the scheme is suitable for low-brightness illumination sources and has stronger anti-interference performance for ranging signal detection in complex environments. At present, the optimal quantum receiver design still requires further research, but many theoretical models and experiments of suboptimal receivers have made significant progress. Preliminary theoretical analysis and recent experiments show that the proposed navigation ranging scheme is feasible and can be further applied to quantum navigation and positioning systems in the future.