Figure 2
From: A stochastic evaluation of quantum Fisher information matrix with generic Hamiltonians
Quantum Fisher information for single magnetic field estimation. Quantum Fisher information \(Q(\phi )\) as a function of the interaction time t for different choices of ϕ, as shown in the figure. The solid curves are exact results from theoretical analysis Eq. (15), the dashed curves are obtained from the Trotter-Suzuki transformation and Stand.PSR, and the dotted curves are obtained from the Stoc.PSR. It can be observed that \(Q(\phi )\) varies with time t and reaches its maximum at \(t = \pi /2\). More importantly, the results show that the Stoc.PSR agrees with the exact analysis while the Stand.PSR gradually deviates from the exact one. The mean-square error (MSE) are plotted as error bars and error areas in the figure. They are systematic errors that caused by different calculation methods