  Current laser-interferometric gravitational wave detectors suffer from a
fundamental limit to their precision due to the displacement noise of optical
elements contributed by various sources. Several schemes for Displacement-Noise
Free Interferometers (DFI) have been proposed to mitigate their effects. The
idea behind these schemes is similar to decoherence-free subspaces in quantum
sensing i.e. certain modes contain information about the gravitational waves
but are insensitive to the mirror motion (displacement noise). In this paper,
we derive quantum precision limits for general DFI schemes, including optimal
measurement basis and optimal squeezing schemes. We introduce a triangular
cavity DFI scheme and apply our general bounds to it. Precision analysis of
this scheme with different noise models shows that the DFI property leads to
interesting sensitivity profiles and improved precision due to noise mitigation
and larger gain from squeezing.
