Geometric measure of quantum discord and total quantum correlations in a N-partite quantum state

TL;DR

This paper extends the geometric measure of quantum discord and total quantum correlations to general N-partite quantum states, providing explicit, experimentally implementable formulas for N-qubit systems.

Contribution

It introduces generic forms and exact formulas for the geometric measure of quantum discord and total correlations in N-partite quantum states, advancing quantification methods.

Findings

Derived explicit formulas for N-qubit states.

Extended geometric quantum discord to N-partite systems.

Formulas are experimentally implementable.

Abstract

Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. \textbf{88}, 017901 (2001)], is a measure of the discrepancy between quantum versions of two classically equivalent expressions for mutual information and is found to be useful in quantification and application of quantum correlations in mixed states. It is viewed as a key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. An early step toward the quantification of quantum discord in a quantum state was by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105,190502 (2010)] who introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. Recently, Luo and Fu [Phys. Rev. A \textbf{82}, 034302 (2010)] introduced a generic form of the geometric measure of quantum discord for a bipartite quantum state. We extend these results and find generic forms of the geometric measure of quantum discord and total quantum correlations in a general N-partite quantum state. Further, we obtain computable exact formulas for the geometric measure of quantum discord and total quantum correlations in a N-qubit quantum state. The exact formulas for the $N$-qubit quantum state are experimentally implementable.