Quantum parameter estimation in a spin-boson dephasing quantum system by periodical projective measurements

In this paper, we explore how to estimate the phase damping parameter γ and the tunneling amplitude parameter △ from a spin-boson dephasing quantum model by periodical projective measurements. The preparation of initial states is accomplished by performing the period measurements in our scheme. The parameter γ can be always estimated when projective measurement bases are chosen as θ=π/2 and φ=0. Based on the estimated value of γ and the interval information of △, we can select another measurement bases (θ=π/4 and φ=π/2) to obtain the estimated value of △. A coherent control is indispensable to estimate △ if γ is in the interval of △; whereas the control is not necessary if γ is out of the known interval of △. We establish the relation between the optimal period time and the parameter γ or △ in terms of Fisher information. Although the optimal measurement period cannot be selected beforehand, the aforementioned relation can be utilized to adjust the measurement period to approach the optimal one.