Analytical solutions and criteria for the quantum discord of two-qubit X-states

TL;DR

This paper provides analytical formulas and criteria for calculating quantum discord in two-qubit X-states, simplifying what is usually a complex optimization process, and validates these formulas against numerical results.

Contribution

It introduces the first comprehensive analytical solutions for quantum discord in general X-states and establishes criteria for their validity, enhancing computational efficiency.

Findings

Analytical solutions match numerical calculations closely.

Parameter regions for different solutions are identified.

Formalism applies to symmetric and arbitrary X-states.

Abstract

Except for a few special states, computing quantum discord remains a complicated optimization process. In this paper we present analytical solutions for computing quantum discord of the most general class of X-states and the criteria for each analytical solution to be valid. We discuss parameter regions that correspond to different analytical solutions and explain the underlying reasons for such structure to exist. We apply our formalism to study both arbitrary X-states and X-states with certain symmetries. We find that our analytical formalism is in excellent agreement with numerical calculation of quantum discord in both cases.