# Entanglement-Enhanced Lidars for Simultaneous Range and Velocity Measurements

## TL;DR

This paper introduces two entanglement-based lidar systems that significantly improve simultaneous range and velocity measurements, surpassing classical limits and achieving Heisenberg-limited accuracy under ideal conditions.

## Contribution

The paper presents novel entanglement-enhanced lidar designs that outperform classical methods in measuring range and velocity, including one that surpasses the Arthurs-Kelly limit and another achieving Heisenberg-limited precision.

## Key findings

- First lidar surpasses Arthurs-Kelly limit without background light
- Second lidar achieves Heisenberg-limited accuracy in ideal conditions
- Entanglement and a specific unitary transformation are key to enhancements

## Abstract

Lidar is a well known optical technology for measuring a target's range and radial velocity. We describe two lidar systems that use entanglement between transmitted signals and retained idlers to obtain significant quantum enhancements in simultaneous measurement of these parameters. The first entanglement-enhanced lidar circumvents the Arthurs-Kelly uncertainty relation for simultaneous measurement of range and radial velocity from detection of a single photon returned from the target. This performance presumes there is no extraneous (background) light, but is robust to the roundtrip loss incurred by the signal photons. The second entanglement-enhanced lidar---which requires a lossless, noiseless environment---realizes Heisenberg-limited accuracies for both its range and radial-velocity measurements, i.e., their root-mean-square estimation errors are both proportional to $1/M$ when $M$ signal photons are transmitted. These two lidars derive their entanglement-based enhancements from use of a unitary transformation that takes a signal-idler photon pair with frequencies $\omega_S$ and $\omega_I$ and converts it to a signal-idler photon pair whose frequencies are $(\omega_S + \omega_I)/2$ and $\omega_S-\omega_I$. Insight into how this transformation provides its benefits is provided through an analogy to superdense coding.