Biasing quantum trajectories for enhanced sensing

Quantum continuous measurement strategies are an essential element in many modern sensing technologies, leading to potentially enhanced estimation of unknown physical parameters. In such schemes, continuous monitoring of the quantum system, which encodes the parameters of interest, gives rise to different quantum trajectories conditioned on the measurement outcomes which carry information on the parameters themselves. Importantly, different trajectories carry different amounts of information, i.e., they are more or less sensitive to the unknown parameters of interest. In this work, we propose an approach on how to systematically engineer the quantum open-system dynamics in order to increase the probability of obtaining trajectories of high sensitivity. We focus on the simplest case scenario of a single two-level system interacting with ancillas, which are in turn measured using the discretized version of continuous monitoring. We analyze the performance of our protocol and demonstrate that it may lead to a substantial enhancement of sensitivity, as quantified by the classical Fisher information, even when applied to such small system sizes, holding the promise of direct implementation in state-of-the-art experimental platforms and large, complex many-body systems.