Stochastic waveform estimation at the fundamental quantum limit

Understand

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well-understood despite it being a widespread task at the frontier of experimental physics.

• State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement, but the optimal quantum protocol for interrogating such linear sensors is not known.
• We derive the fundamental precision limit, the extended channel quantum Cram\'er-Rao bound, and the optimal protocol that attains it.
• In the experimentally relevant regime where losses dominate, we prove that non-Gaussian state preparation and measurements are required for optimality.