  The range and speed of a moving object can be ascertained using the sensing
technique known as light detection and ranging (LiDAR). It has recently been
suggested that quantum LiDAR, which uses entangled states of light, can enhance
the capabilities of LiDAR. Entangled pulsed light is used in prior quantum
LiDAR approaches to assess both range and velocity at the same time using the
pulses' time of flight and Doppler shift. The entangled pulsed light generation
and detection, which are crucial for pulsed quantum LiDAR, are often
inefficient. Here, we study a quantum LiDAR that operates on a
frequency-modulated continuous wave (FMCW), as opposed to pulses. We first
outline the design of the quantum FMCW LiDAR using entangled
frequency-modulated photons in a Mach-Zehnder interferometer, and we
demonstrate how it can increase accuracy and resolution for range and velocity
measurements by $\sqrt{n}$ and $n$, respectively, with $n$ entangled photons.
We also demonstrate that quantum FMCW LiDAR may perform simultaneous
measurements of the range and velocity without the need for quantum pulsed
compression, which is necessary in pulsed quantum LiDAR. Since the generation
of entangled photons is the only inefficient nonlinear optical process needed,
the quantum FMCW LiDAR is better suited for practical implementations.
Additionally, most measurements in the quantum FMCW LiDAR can be carried out
electronically by down-converting optical signal to microwave region.
