  We present a theoretical investigation of a whispering gallery mode (WGM)
resonator coupled to a Mach-Zehnder interferometer (MZI) and show a bimodal
coincidence transmission spectrum when the input state is an indistinguishable
photon pair. This is due to the doubled WGM phase shift experienced by the
path-entangled state in the interferometer. Further, we model the noise in a
WGM resonance shift measurement comparing photon pairs with a coherent state.
At least a four-fold improvement in the signal-to-noise ratio (SNR) is
possible, with clear implications for quantum-enhanced WGM sensing.
