Characterization of qubit chains by Feynman probes
Dario Tamascelli, Claudia Benedetti, Stefano Olivares, Matteo G. A. Paris · Physical Review A · 2016
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 register 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.