  A surprising feature of the Kerr metric is the anisotropy of the speed of
light. The angular momentum of a rotating massive object causes co- and
counter-propagating light paths to move at faster and slower velocities,
respectively as determined by a far-away clock. Based on this effect we derive
ultimate quantum limits for the measurement of the Kerr rotation parameter $a$
using a interferometric set up. As a possible implementation, we propose a
Mach-Zehnder interferometer to measure the "one-way height differential" time
effect. We isolate the effect by calibrating to a dark port and rotating the
interferometer such that only the direction dependent Kerr-metric induced phase
term remains. We transform to the Zero Angular Momentum Observer (ZAMO) flat
metric where the observer see $c=1$. We use this metric and the Lorentz
transformations to calculate the same Kerr phase shift. We then consider
non-stationary observers moving with the planet's rotation, and find a method
for cancelling the additional phase from the classical relative motion, thus
leaving only the curvature induced phase.
