Verification of quantum discord

TL;DR

This paper presents a measurement-based method for verifying quantum discord in bipartite systems, utilizing IC-POVMs and conditional state commutativity, applicable to continuous-variable systems like Gaussian states.

Contribution

Introduces a novel, efficient measurement-based approach for verifying quantum discord, especially suited for continuous-variable systems and Gaussian states.

Findings

Quantum discord can be verified via conditional Wigner functions.

Gaussian states with zero discord are only product states.

Gaussian discord states have nonzero quantum discord.

Abstract

We introduce a measurement-based method for verifying quantum discord of any bipartite quantum system. We show that by performing an informationally complete POVM (IC-POVM) on one subsystem and checking the commutativity of the conditional states of the other subsystem, quantum discord from the second subsystem to the first can be verified. This is an improvement upon previous methods, which enables us to efficiently apply our method to continuous-variable systems, as IC-POVMs are readily available from homodyne or heterodyne measurements. We show that quantum discord for Gaussian states can be verified by checking whether the peaks of the conditional Wigner functions corresponding to two different outcomes of heterodyne measurement coincide at the same point in the phase space. Using this method, we also prove that the only Gaussian states with zero discord are product states; hence, Gaussian states with Gaussian discord have nonzero quantum discord.