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

TL;DR

This paper investigates the reliability of fidelity as a figure of merit in quantum state reconstruction, revealing that high fidelity does not always indicate similar physical properties, especially in quantum-to-classical transitions.

Contribution

It provides an experimental analysis of fidelity's significance in quantum tomography for both discrete and continuous variable systems, highlighting its limitations.

Findings

High fidelity can correspond to states with opposite physical properties.

Fidelity may not accurately reflect nonclassicality, entanglement, or quantum discord.

Fidelity's limitations are demonstrated in quantum-to-classical transition scenarios.

Abstract

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, focussing 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 details 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.