Characterization of qubit chains by Feynman probes

We address the characterization of qubit chains and assess the performances of local measurements compared to those provided by Feynman probes, i.e. nonlocal measurements realized by coupling a single qubit regis- ter to the chain. We show that local measurements are suitable to estimate small values of the coupling and that a Bayesian strategy may be successfully exploited to achieve optimal precision. For larger values of the coupling Bayesian local strategies do not lead to a consistent estimate. In this regime, Feynman probes may be exploited to build a consistent Bayesian estimator that saturates the Cram\'er-Rao bound, thus providing an effective characterization of the chain. Finally, we show that ultimate bounds to precision, i.e. saturation of the quantum Cram\'er-Rao bound, may be achieved by a two-step scheme employing Feynman probes followed by local measurements.