Necessary and sufficient condition for saturating the upper bound of quantum discord

TL;DR

This paper characterizes the conditions under which quantum discord reaches its maximum possible value in bipartite quantum states, revealing a fundamental trade-off with classical correlations and implications for quantum information processing.

Contribution

It provides an explicit criterion for quantum states that saturate the upper bound of quantum discord using the Araki-Lieb inequality, linking quantum and classical correlations.

Findings

Identifies the states that saturate the quantum discord upper bound.

Shows that saturation prevents additional correlations with the environment.

Establishes a trade-off between classical and quantum correlations in tripartite states.

Abstract

We revisit the upper bound of quantum discord given by the von Neumann entropy of the measured subsystem. Using the Koashi-Winter relation, we obtain a trade-off between the amount of classical correlation and quantum discord in the tripartite pure states. The difference between the quantum discord and its upper bound is interpreted as a measure on the classical correlative capacity. Further, we give the explicit characterization of the quantum states saturating the upper bound of quantum discord, through the equality condition for the Araki-Lieb inequality. We also demonstrate that the saturating of the upper bound of quantum discord precludes any further correlation between the measured subsystem and the environment.