  We consider parameter estimations with probes being the boundary
driven/dissipated non- equilibrium 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.

Quantum Physics;Strongly Correlated Electrons;Exactly Solvable and Integrable Systems;Applications