The effect of non-selective measurement on the parameter estimation within spin-spin model

TL;DR

This paper explores how non-selective measurements and initial correlations in a spin-spin model can significantly enhance the accuracy of parameter estimation, such as bath temperature and coupling strength, compared to traditional projective measurements.

Contribution

It demonstrates that non-selective measurements and initial correlations can improve parameter estimation accuracy in spin-spin models, surpassing traditional projective measurement methods.

Findings

Non-selective measurement improves estimation accuracy by orders of magnitude.

Initial correlations significantly enhance quantum Fisher information.

Unitary preparation of initial states outperforms projective measurement in certain scenarios.

Abstract

We investigate the role of non-selective measurement on the estimation of system-environment parameters. Projective measurement is the popular method of initial state preparation which always prepares a pure state. However, in various physical situations of physical interest, this selective measurement becomes unrealistic. In this paper, we 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 where a central two-level system (probe) interacts with the collections of two-level systems (bath). A probe interacts with a bath and attains a thermal equilibrium state, 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 a phenomenal 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 via non-selective measurement and by incorporating the effect of initial correlations.