Quantum measurements in spin-boson model under non-Markovian environment

We propose a control approach of the parameter estimation for a two-level quantum system interacting with a bosonic reservoir considering non-Markovian open, dissipative quantum system. We show that the precision of the estimation significantly affected and behaves differently within the framework of the markovian and non-Markovian regimes. The influence of memory effects for an Ohmic reservoir with Lorentz-Drude regularization on the estimation-parameter precision are numerically demonstrated under the following three conditions: ω0⪡ωc, ω0≈ωc or ω0⪢ωc, where ω0 is the characteristic frequency of the two-level system, and ωc is the cut-off frequency of Ohmic reservoir. We investigate the precision rate in high temperature, intermediate temperature, and low temperature reservoirs for various values of the ratio r=ωc/ω0 considering manifold external fields. We reveal that the enhancement and preservation of the measurement precision, highly depend on the combination of the external control field, reservoir parameters, and non-Markovian effects.