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.