Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems

We experimentally address the significance of fidelity as a figure of merit in quantum state reconstruction of discrete (DV) and continuous-variable (CV) quantum optical systems. In particular, we analyze the use of fidelity in quantum homodyne tomography of CV states and maximum-likelihood polarization tomography of DV ones, focusing attention on nonclassicality, entanglement, and quantum discord as a function of fidelity to a target state. Our findings show that high values of fidelity, despite well quantifying geometrical proximity in the Hilbert space, may be obtained for states displaying opposite physical properties, e.g., quantum or semiclassical features. In particular, we analyze in detail the quantum-to-classical transition for squeezed thermal states of a single-mode optical system and for Werner states of a two-photon polarization qubit system.