The role of initial system-environment correlations in the accuracies of parameters within spin-spin model

TL;DR

This paper demonstrates that initial system-environment correlations significantly enhance the precision of estimating environment parameters, such as temperature and coupling strength, in a spin-spin quantum model.

Contribution

It introduces a method to incorporate initial correlations in a spin-spin model, markedly improving parameter estimation accuracy using quantum Fisher information.

Findings

Initial correlations improve temperature estimation accuracy by orders of magnitude.

Strong coupling regimes benefit from initial correlations for better precision.

Correlations notably enhance estimation accuracy at low temperatures.

Abstract

We investigate the effect of initial system-environment correlations to improve the estimation of environment parameters. By employing various physical situations of interest, we present results for the environment temperature and system-environment coupling strength. We consider the spin-spin model whereby a probe (a small controllable quantum system) interacts with a bath of quantum spins and attains a thermal equilibrium state. A projective measurement is then performed to prepare the initial state and allow it to evolve unitarily. The properties of the environment are imprinted upon the dynamics of the probe. The reduced density matrix of the probe state contains a modified decoherence factor and dissipation. This additional factor acts in such a way to improve the estimation of the environment parameters, as quantified by the quantum Fisher information (QFI). In the temperature estimation case, our results are promising as one can improve the precision of the estimates by orders of magnitude by incorporating the effect of initial correlations. The precision increases in the strong coupling regime even if the nearest neighbours' interaction is taken into account. In the case of coupling strength, interestingly the accuracy was found to be continuously increasing in both with and without correlations cases. More importantly, one can see the noticeable role of correlations in improving precision, especially at low temperatures.