To detect a stealth target, one may directly probe it with a single photon and analyze the reflected signals. The efficiency of such conventional detection scheme can potentially be enhanced by quantum illumination, where entanglement is exploited to break the classical limits. The question is what is the optimal signal state for achieving the detection limit? Here, we address this question in a general discrete model, and derive a complete set of analytic solutions. For one-shot detection, the parameter space can be classified into three distinct regions, in the form of a “phase diagram” for both conventional and quantum illumination. Interestingly, whenever the reflectivity of the target is less than some critical value, all received signals become useless, which is true even if entangled resources are employed. However, there does exist a region where quantum illumination can provide advantages over conventional illumination; there, the optimal signal state is an entangled state with an entanglement spectrum inversely proportional to the spectrum of the environmental noise state and is, surprisingly, independent of the occurrence probability and the reflectivity of the object. The entanglement of the ideal probe state increases with the entropy of the environment; it becomes more entangled as the temperature of the environment increases. Finally, we show that the performance advantage cannot be fully characterized by any measure of quantum correlation, unless the environment is a complete mixed state.

为了检测隐身目标，可以直接用单个光子探测隐身目标并分析反射信号。量子照明可以潜在地提高这种常规检测方案的效率，其中利用纠缠来突破经典极限。问题是达到检测极限的最佳信号状态是什么？在这里，我们以一般的离散模型解决此问题，并得出一整套解析解。对于单次检测，可以将参数空间以“相图”的形式分为三个不同的区域，用于常规照明和量子照明。有趣的是，每当目标的反射率小于某个临界值时，所有接收到的信号都将变得无用，即使使用了纠缠的资源也是如此。然而，确实存在一个区域，在该区域中量子照明可以提供优于常规照明的优势；在这里，最佳信号状态是一个纠缠态，其纠缠光谱与环境噪声态的光谱成反比，并且令人惊讶地，它与对象的出现概率和反射率无关。理想探针状态的纠缠度随环境的熵而增加；随着环境温度的升高，它变得更加纠结。最后，我们证明，除非环境为完全混合态，否则任何量子相关措施都无法完全表征性能优势。最佳信号状态是一个纠缠态，其纠缠光谱与环境噪声态的光谱成反比，并且令人惊讶地，它与对象的出现概率和反射率无关。理想探针状态的纠缠度随环境的熵而增加；随着环境温度的升高，它变得更加纠结。最后，我们证明，除非环境为完全混合态，否则任何量子相关措施都无法完全表征性能优势。最佳信号状态是一个纠缠态，其纠缠光谱与环境噪声态的光谱成反比，并且令人惊讶地，它与对象的出现概率和反射率无关。理想探针状态的纠缠度随环境的熵而增加；随着环境温度的升高，它变得更加纠结。最后，我们证明，除非环境为完全混合态，否则任何量子相关性度量都无法完全表征性能优势。随着环境温度的升高，它变得更加纠结。最后，我们证明，除非环境为完全混合态，否则任何量子相关性度量都无法完全表征性能优势。随着环境温度的升高，它变得更加纠结。最后，我们证明，除非环境为完全混合态，否则任何量子相关性度量都无法完全表征性能优势。