Precision Quantum Parameter Inference with Continuous Observation

Quantum Parameter Estimation (QPE) is important from the perspective of both fundamental quantum research and various practical applications of quantum technologies such as for developing optimal quantum control strategies. Standard and traditional methods for QPE involve projective measurements on thousands of identically prepared quantum systems. However, these methods face limitations, particularly in terms of the required number of samples and the associated experimental resources. In this work, we present a novel method for precise QPE that diverges from conventional techniques, employs continuous measurements, and enables accurate QPE with a single quantum trajectory. In an application, we demonstrate the use of the method for the task of parameter estimation and force sensing of a levitated nanoparticle.