  We analyze a fiber-optic gyroscope design enhanced by the injection of
quantum-optical squeezed vacuum into a fiber-based Sagnac interferometer. In
the presence of fiber loss, we compute the maximum attainable enhancement over
a classical, laser-driven fiber-optic gyroscope in terms of the angular
velocity estimate variance from a homodyne measurement. We find a constant
enhancement factor that depends on the degree of squeezing introduced into the
system but has diminishing returns beyond $10$--$15$ dB of squeezing. Under a
realistic constraint of fixed total fiber length, we show that segmenting the
available fiber into multiple Sagnac interferometers fed with a
multi-mode-entangled squeezed vacuum, thereby establishing quantum entanglement
across the individual interferometers, improves the rotation estimation
variance by a factor of $e\approx2.718$.
