  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.
