We study the efficiency of quantum tomographic reconstruction where the system under investigation (quantum target) is indirectly monitored by looking at the state of a quantum probe that has been scattered off the target. In particular we focus on the state tomography of a qubit through a one-dimensional scattering of a probe qubit, with a Heisenberg-type interaction. Via direct evaluation of the associated quantum Cram\'{e}r-Rao bounds, we compare the accuracy efficiency that one can get by adopting entanglement-assisted strategies with that achievable when entanglement resources are not available. Even though sub-shot noise accuracy levels are not attainable, we show that quantum correlations play a significant role in the estimation. A comparison with the accuracy levels obtainable by direct estimation (not through a probe) of the quantum target is also performed.
@article{arxiv.1107.5545,
title = {Entanglement-assisted tomography of a quantum target},
author = {A. De Pasquale and P. Facchi and V. Giovannetti and K. Yuasa},
journal= {arXiv preprint arXiv:1107.5545},
year = {2012}
}