Multi-objective optimization in quantum parameter estimation

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved,it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives:(1) maximizing the Fisher information, improving the parameter estimation precision, and(2)minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified ε-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.