We propose a quantum ranging protocol to determine the distance between an
observer and a target at the line of sight in the curved spacetime of the
Earth. Different from a quantum illumination scheme, here we employ a multiple
quantum hypothesis testing to determine the existence and the location of the
target at the same time. In the proposed protocol, the gravitational effect of
the Earth influences the propagation of photons, and therefore has an
observable impact on the performance of quantum ranging tasks. It is shown that
the maximum potential advantages of the quantum ranging strategy in the curved
spacetime has distinct superiority over its counterpart in the flat spacetime.
This is because the effect of the gravitational red-shift and blue-shift on the
entangled signal beam can cancel each other, while the thermal signal only
suffers form the gravitational blue-shift effect. It is shown that increasing
the number of transmitted modes can promote the maximum potential advantage of
quantum ranging in the curved spacetime. However, the maximum potential
advantage of quantum ranging in the curved spacetime can not been raised
sharply by dividing the range into multiple slices.
