Analytical expression of Genuine Tripartite Quantum Discord for Symmetrical X-states

TL;DR

This paper derives an analytical formula for genuine tripartite quantum discord in symmetrical X-states, aiding the quantification of quantum correlations in three-qubit systems and potentially extending to more complex multipartite states.

Contribution

It provides the first analytical expression for GTQD in symmetrical X-states, facilitating easier computation and understanding of quantum correlations in multipartite systems.

Findings

Successfully derived analytical GTQD expression for symmetrical X-states.

Validated the formula on GHZ and maximally mixed states.

Provides a methodological guideline for analyzing quantum discord in larger systems.

Abstract

The study of classical and quantum correlations in bipartite and multipartite systems is crucial for the development of quantum information theory. Among the quantifiers adopted in tripartite systems, the genuine tripartite quantum discord (GTQD), estimating the amount of quantum correlations shared among all the subsystems, plays a key role since it represents the natural extension of quantum discord used in bipartite systems. In this paper, we derive an analytical expression of GTQD for three-qubit systems characterized by a subclass of symmetrical X-states. Our approach has been tested on both GHZ and maximally mixed states reproducing the expected results. Furthermore, we believe that the procedure here developed constitutes a valid guideline to investigate quantum correlations in form of discord in more general multipartite systems.