Quantum metrology with non-equilibrium steady states of quantum spin chains

TL;DR

This paper explores quantum metrology using non-equilibrium steady states of spin chains, demonstrating superlinear scaling of Fisher information and phase-dependent sensitivity improvements for parameter estimation.

Contribution

It introduces a novel approach to quantum metrology employing boundary-driven spin chains and analyzes the Fisher information scaling in different phases.

Findings

Superlinear Fisher information scaling with system size.

Phase-dependent transitions affecting estimation precision.

Enhanced sensitivity for anisotropy parameter estimation.

Abstract

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.