Achieving the fundamental quantum limit of linear waveform estimation

Sensing a classical signal using a linear quantum device is a pervasive application of quantum-enhanced measurement. The fundamental precision limits of linear waveform estimation, however, are not fully understood. In certain cases, there is an unexplained gap between the known waveform-estimation Quantum Cram\'er-Rao Bound and the optimal sensitivity from quadrature measurement of the outgoing mode from the device. We resolve this gap by establishing the fundamental precision limit, the waveform-estimation Holevo Cram\'er-Rao Bound. The standard homodyne measurement does not saturate this bound, we propose measurement schemes that saturate it and study possible experimental realizations of them. We apply our results to detuned gravitational-wave interferometry to accelerate the search for post-merger remnants from binary neutron-star mergers. For several applications, our scheme can improve the signal-to-noise ratio by a factor of $\sqrt2$.