Optimal State Preparation for Impulse Estimation in Gaussian Quantum Systems
This work provides a method to improve impulse estimation in quantum metrology, relevant for nanomechanical resonators and levitated nanoparticles.
The authors develop an optimal control strategy to enhance impulse disturbance estimation in Gaussian quantum systems, achieving up to a factor of two reduction in estimation variance compared to steady-state operation.
We present an optimal control-based strategy to enhance the estimation of impulse-like disturbances in continuously monitored linear classical and quantum systems by exploiting non-equilibrium states. Using optimal estimation techniques for linear Gaussian systems to collect information from the temporal vicinity of the disturbance, we cast the minimization of disturbance estimation uncertainty as a nonlinear optimal control problem over time-dependent system parameters. The resulting method dynamically shapes the estimation covariances through parametric modulation, maximizing information gain at a known impulse time. This differs fundamentally from conventional squeezing protocols using periodic modulation that effectively degrade inference of impulse-like disturbances. Applied to nanomechanical resonators and levitated nanoparticles, optimal parametric driving reduces estimation variance by up to a factor of two relative to steady-state operation