  We study the effect of the acceleration of the observer on a parameter
estimation protocol using NOON states. An inertial observer, Alice, prepares a
NOON state in Unruh modes of the quantum field, and sends it to an accelerated
observer, Rob. We calculate the quantum Fisher information of the state
received by Rob. We find the counter-intuitive result that the single rail
encoding outperforms the dual rail. The NOON states have an optimal $N$ for the
maximum information extractable by Rob, given his acceleration. This optimal
$N$ decreases with increasing acceleration.
