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 Cramér-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 Cramér-Rao bound, and how to achieve it using a nonstationary measurement. We apply our results to detuned gravitational-wave interferometry to accelerate the search for postmerger remnants from binary neutron-star mergers. If we have an unequal weighting between estimating the signal’s power and phase, then we propose how to further improve the signal-to-noise ratio by a factor of $\sqrt{2}$ using this nonstationary measurement.

Figure 1

(a) A linear quantum device coupled to a classical signal. (b) For example, a gravitational-wave interferometer.

Figure 2

(a) HCRB versus the commutator and weight. (b) HCRB versus the weight for different commutators.

Figure 3

(a) Phase-modulated balanced homodyne readout. (b) Asymmetric beam splitter with power reflectivity $\cos (\overline{\varphi }{)}^2$.

Figure 4

Strain sensitivity for the detuned LIGO-like interferometer versus frequency for different weights in (top row) effective amplitude spectral density units and (bottom row) ratio to the QCRB.