  Squeezed states of light have been successfully employed in interferometric
gravitational-wave detectors to reduce quantum noise, thus becoming one of the
most promising options for extending the astrophysical reach of the generation
of detectors currently under construction worldwide. In these advanced
instruments, quantum noise will limit sensitivity over the entire detection
band. Therefore, to obtain the greatest benefit from squeezing, the injected
squeezed state must be filtered using a long-storage-time optical resonator, or
"filter cavity", so as to realise a frequency dependent rotation of the
squeezed quadrature. Whilst the ultimate performance of a filter cavity is
determined by its storage time, several practical decoherence and degradation
mechanisms limit the experimentally achievable quantum noise reduction. In this
paper we develop an analytical model to explore these mechanisms in detail. As
an example, we apply our results to the 16 m filter cavity design currently
under consideration for the Advanced LIGO interferometers.
