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 Cramer-Rao bound, thus providing an effective characterization of the chain. Finally, we show that ultimate bounds to precision, i.e. saturation of the quantum Cramer-Rao bound, may be achieved by a two-step scheme employing Feynman probes followed by local measurements.
A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix playing t
he role of the density matrix and homodyne detection providing Stern-Gerlach-like projections. The major difference stems from a different character of relevant noises: while the statistics of Stern-Gerlach-like measurements is governed by binomial statistics, the detection of quadrature variances correspond to chi-square statistics. For Gaussian and near Gaussian states the suggested method provides, compared to standard tomography techniques, more stable and reliable reconstructions. In addition, by putting together reconstruction methods for Gaussian and arbitrary states, we obtain a tool to detect the non-Gaussian character of optical signals.
