Quantum-limited estimation of range and velocity

TL;DR

This paper applies quantum metrology to determine the fundamental limits of simultaneously estimating range and velocity in radar and lidar systems, revealing advantages of entangled states for improved precision.

Contribution

It introduces a quantum metrology framework for joint range and velocity estimation, showing entanglement can relax or eliminate the trade-off between these parameters.

Findings

Entangled probe states improve joint estimation precision.

Trade-off between position and velocity estimation is relaxed with entanglement.

Near-optimal joint estimation is possible without entanglement for closely spaced targets.

Abstract

The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity (through Doppler frequency shifts) of a target are inversely related to each other, and dictated by the bandwidth of the signal. Here we use the theoretical toolbox of multi-parameter quantum metrology to determine the ultimate precision of the simultaneous estimation of range and velocity. We consider the case of a single target as well as a pair of closely separated targets. In the latter case, we focus on the relative position and velocity. We show that the trade-off between the estimation precision of position and velocity is relaxed for entangled probe states, and is completely lifted in the limit of infinite entanglement. In the regime where the two targets are close to each other, the relative position and velocity can be estimated nearly optimally and jointly, even without entanglement, using the measurements determined by the symmetric logarithmic derivatives.