Quantum metrology with nonequilibrium steady states of quantum spin chains
Ugo Marzolino, Tomaž Prosen · Physical Review A · 2014
We consider parameter estimations with probes being the boundary-driven or dissipated nonequilibrium steady states of $XXZ$ spin-$1/2$ chains. The parameters to be estimated are the dissipation coupling and the anisotropy of the spin-spin interaction. In the weak-coupling regime we compute the scaling of the Fisher information, i.e., the inverse best sensitivity among all estimators, with the number of spins. We find superlinear scalings and transitions between the distinct isotropic and anisotropic phases. We also look at the best relative error, which decreases with the number of particles faster than the shot-noise only for the estimation of anisotropy.