Geometric global quantum discord of two-qubit X states

TL;DR

This paper derives analytical formulas for geometric quantum discord and geometric global quantum discord in two-qubit X states, providing concrete examples and establishing that the geometric quantum discord is a tight lower bound of the global measure.

Contribution

The paper presents the first analytical formulas for geometric quantum discord and global discord in two-qubit X states, enhancing understanding of quantum correlations.

Findings

Derived analytical formulas for both discord measures.

Provided five concrete examples demonstrating the formulas.

Proved geometric quantum discord is a tight lower bound of global discord.

Abstract

Xu [Jianwei Xu, J. Phys. A: Math. Theor. 45 405304 (2012)] generalized geometric quantum discord [B.Dakic, V. Vedral, and C . Brukner, Phys. Rev. Lett. 105 190502 (2010)] to multipartite states and proposed the geometric global quantum discord. In this paper, we first derive the analytical formulas of the geometric global quantum discord and geometric quantum discord for two-qubit X states, respectively. Second, we give five concrete examples to demonstrate the use of our formulas. Finally, we prove that the geometric quantum discord is a tight lower bound of the geometric global quantum discord.