General Relativity and Quantum Cosmology (gr-qc)

Abstract: Detecting kilohertz gravitational waves from the post-merger remnants of binary neutron-star mergers could enhance our understanding of extreme matter. To enable this detection, a gravitational-wave interferometer can be detuned to increase its kilohertz sensitivity. The precision limits of detuned interferometers and other cavity--based quantum sensors, however, are not well understood. The sensitivity of the standard variational readout scheme does not reach the waveform-estimation Quantum Cram\'er-Rao Bound. We establish the fundamental precision limit, the waveform-estimation Holevo Cram\'er-Rao Bound, by identifying the incompatibility of the na\"ive estimates of the signal's cosine and sine phases. For an equal weighting between the phases, we prove that the standard scheme is indeed optimal. For unequal weights, however, we propose an experimental realisation of a new measurement scheme to significantly improve the sensitivity. This scheme could facilitate kilohertz gravitational-wave astronomy and has broader applications to detuned cavity--based quantum metrology.