Hilbert-Schmidt measure of pairwise quantum discord for three-qubit $X$ states

TL;DR

This paper introduces an analytical approach using Hilbert-Schmidt distance to quantify pairwise quantum correlations in three-qubit $X$ states, including special classes like W, GHZ, and Bell states, and examines their monogamy properties.

Contribution

It provides explicit formulas for geometric quantum discord in three-qubit $X$ states and analyzes their monogamy relations, advancing understanding of quantum correlations.

Findings

Derived analytical expressions for geometric quantum discord.

Analyzed monogamy properties of quantum discord in specific three-qubit states.

Focused on special classes including W, GHZ, and Bell states.

Abstract

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit $X$ states. They include three-qubit states of ${\rm W}$, ${\rm GHZ}$ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems.