Systematic calibration error requirements for gravitational-wave detectors via the Cram\'{e}r-Rao bound

Gravitational-wave (GW) laser interferometers such as Advanced LIGO transduce spacetime strain into optical power fluctuation. Converting this optical power fluctuations back into an estimated spacetime strain requires a calibration process that accounts for both the interferometer's optomechanical response and the feedback control loop used to control the interferometer test masses. Systematic errors in the calibration parameters lead to systematic errors in the GW strain estimate, and hence to systematic errors in the astrophysical parameter estimates in a particular GW signal. In this work we examine this effect for a GW signal similar to GW150914, both for a low-power detector operation similar to the first and second Advanced LIGO observing runs and for a higher-power operation with detuned signal extraction. We set requirements on the accuracy of the calibration such that the astrophysical parameter estimation is limited by errors introduced by random detector noise, rather than calibration systematics. We also examine the impact of systematic calibration errors on the possible detection of a massive graviton.