Quantum parameter estimation and coherent control with a time-dependent Hamiltonian

We present our theoretical results on quantum metrology of a general parameter when the Hamiltonian is time-dependent. We obtain the optimal solution to the quantum Fisher information, and show that coherent control can give an advantage in maximizing it. We derive the optimal Hamiltonian control required, and with a minimal example of a spin-1/2 particle in a rotating magnetic field, we find that the fundamental limit of $T^2$ time scaling for the quantum Fisher information of time-independent Hamiltonian can be exceeded when the Hamiltonian is time-dependent, which reaches $T^4$ time scaling in estimating the rotation frequency of the field. This may be understood intuitively as the acquired quantum phase accelerating in time. Reference: arXiv:1606.02166