  Quantum illumination can utilize entangled light to detect the
low-reflectivity target that is hidden in a bright thermal background. This
technique is applied to the detection of an object in the curved spacetime of
the Earth, in order to explore how the curvature of spacetime affects quantum
illumination. It is found that the spatial quantum illumination with entangled
state transmitter outperforms that with coherent-state transmitter in the
near-Earth curved spacetime. Moreover, either the quantum illumination system
or the coherent-state system is employed, and gravity can enhance the spacetime
target detection by reducing the thermal signal at the receiver. Besides, our
model in principle can be applied to microwave quantum illumination and thus
provides, to some degree, a theoretical foundation for the upcoming spatial
quantum radar technologies.
