Quantum-Enhanced Doppler Lidar

We propose a quantum-enhanced protocol to estimate the radial velocity v of a moving target, using an optical frequency-entangled squeezed state composed of a signal and an idler beam as a probe state. The signal beam illuminates the moving object and it is reflected with its frequency shifted due to the Doppler effect. Then, a measurement on signal and idler beams is performed to estimate the velocity of the object. We aim at benchmarking this protocol against the classical one, which comprises a coherent state with the same pulse duration and energy illuminating the object. Indeed, employing squeezing and frequency entanglement as quantum resources provides to a precision enhancement in the estimation of the velocity of the object. We identify three distinct parameter regimes. First, the frequency entanglement-dominant regime, where the quantum and the classical protocols perform equally well. Second, the squeezing-dominant regime, with a quantum advantage that is higher than the standard quantum limit. Third, the mixed regime, where both squeezing and frequency entanglement are comparable and the proposed quantum protocol attains the Heisenberg limit. Losses in the signal beam are considered for the high-squeezing regime. The protocol shows resilience, outperforming the classical protocol for all channel transmissivities. We show that an optimal measurement to achieve these results in the lossless case is frequency-resolved photon-number counting.