Quantum discord for the general two-qubit case

TL;DR

This paper introduces a generalized mathematical framework to compute quantum discord in two-qubit systems, providing universal solutions and analytical results for specific subclasses, advancing the understanding of quantum correlations.

Contribution

It generalizes the method for calculating quantum discord using the Choi-Jamiolkowski isomorphism and proves the existence of finite universal solutions for the transcendental equations involved.

Findings

Transcendental equations for quantum discord have finite universal solutions.

Analytical solutions are obtained for a subclass of X states.

The method generalizes previous approaches to two-qubit quantum discord calculation.

Abstract

Recently, Girolami and Adesso have demonstrated that the calculation of quantum discord for two-qubit case can be viewed as to solve a pair of transcendental equation (Phys. Rev. A, {\bf 83}, 052108(2011)). In present work, we introduce the generalized Choi-Jamiolkowski isomorphism and apply it as a convenient tool for constructing transcendental equations. For the general two-qubit case, we show that the transcendental equations always have a finite set of universal solutions, this result can be viewed as a generalization of the one get by Ali, Rau, and Alber (Phys. Rev. A, {\bf 81}, 042105 (2010)). For a subclass of $X$ state, we find the analytical solutions by solving the transcendental equations.