  Numerous quantum mechanical schemes have been proposed that are intended to
improve the sensitivity to rotation provided by the classical Sagnac effect in
gyroscopes. A general metric is needed that can compare the performance of the
new quantum systems with the classical systems. The fidelity (Shannon mutual
information between the measurement and the rotation rate) is proposed as a
metric that is capable of this comparison. A theoretical upper bound is derived
for the fidelity of an ideal classical Sagnac gyroscope. This upper bound for
the classical Sagnac gyroscope should be used as a benchmark to compare the
performance of proposed enhanced classical and quantum rotation sensors. In
fact, the fidelity is general enough to compare the quality of two different
apparatuses (two different experiments) that attempt to measure the same
quantity.
