Optimal control for quantum detectors

Quantum systems are promising candidates for sensing of weak signals as they can provide unrivaled performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal to noise ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal control to detect an external signal in the presence of background noise using a quantum sensor. We show this by considering the time-dependent control using the filter function formalism, and we use this formalism to derive the optimal protocol that maximizes the signal-to-noise ratio for the quantum detector. Interestingly, this optimal solution is the simple and well-known spin-locking control scheme. We further show, using numerical techniques, that this result is robust even when lifting some of our assumptions. These results show how that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.