  We found that the measurement sensitivity of an optical integrating gyroscope
is fundamentally limited due to ponderomotive action of the light leading to
the standard quantum limit of the rotation angle detection. The uncorrelated
quantum fluctuations of power of clockwise and counterclockwise electromagnetic
waves result in optical power-dependent uncertainty of the angular gyroscope
position. We also show that, on the other hand, a quantum back action evading
measurement of angular momentum of a gyroscope becomes feasible if proper
measurement strategy is selected. The angle is perturbed in this case. This
observation hints on fundamental inequivalency of integrating and rate
gyroscopes.
