Experimental estimation of quantum discord for polarization qubit and the use of fidelity to assess quantum correlations

TL;DR

This paper experimentally investigates how to estimate quantum discord in polarization qubits, comparing full and partial tomography, and questions the reliability of fidelity as a measure of quantum correlations.

Contribution

It provides an experimental comparison of quantum discord estimation methods and highlights the limitations of fidelity in assessing quantum correlations.

Findings

Partial tomography yields smaller discord for depolarized states.

Fidelity may not reliably reflect quantum discord.

Estimating quantum discord is inherently noisy without an analytic formula.

Abstract

We address the experimental determination of entropic quantum discord for systems made of a pair of polarization qubits. We compare results from full and partial tomography and found that the two determinations are statistically compatible, with partial tomography leading to a smaller value of discord for depolarized states. Despite the fact that our states are well described, in terms of fidelity, by families of depolarized or phase-damped states, their entropic discord may be largely different from that predicted for these classes of states, such that no reliable estimation procedure beyond tomography may be effectively implemented. Our results, together with the lack of an analytic formula for the entropic discord of a generic two-qubit state, demonstrate that the estimation of quantum discord is an intrinsically noisy procedure. Besides, we question the use of fidelity as a figure of merit to assess quantum correlations.