The effect of state preparation on the probe-bath parameters estimation

Abstract Projective measurement is a popular method of initial state preparation, which always prepares a pure state. However, in various physical situations of interest, this selective measurement becomes unrealistic. In this paper, we investigate the role of pulsed measurement (a unitary operation) on the estimation of system-environment parameters and compare the estimation results obtained via projective measurement with the results obtained via unitary operation. We argue that in typical situations, parameters can be estimated with higher accuracy if the initial state is prepared with the unitary operator (a pulse). We consider the spin-spin model in which a central two-level system (probe) interacts with a collection of two-level systems (bath). The probe interacts with the bath and attains thermal equilibrium. Then, via unitary operation, the initial state is prepared which evolves unitarily. The properties of the bath are imprinted on the reduced dynamics. Due to the initial probe-bath correlations present in the thermal equilibrium state, an additional factor arises in the dynamics, which has an important role in the parameter estimation. In this paper, we study the estimation of bath temperature and probe-bath coupling strength which is quantified by the quantum Fisher information. Our results are promising as one can improve the precision of the estimates by orders of magnitude (especially in the coupling strength case) via unitary operation and by incorporating the effect of initial correlations.