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

Characterization of qubit chains by Feynman probes