# Geometric quantum discord for two-qubit X-states. (arXiv:1710.04007v1 [quant-ph])

Geometric quantum discord with Bures distance, a kind of correlations in

geometric point of view, is defined as the minimal Bures distance between the

quantum state and the set of zero-discord states in bipartite quantum system.

Comparing to other geometric distance, Bures distance is monotonous and

Riemannian and the minimal Bures distance to zero-discord states satisfies all

criteria of an discord measure. Furthermore, Bures geometric quantum discord is

closely linked to a minimal error quantum state discrimination. So far,

geometric quantum discord with Bures distance has been calculated explicitly

only for a rather limited set of two-qubit quantum states and expression for

more general quantum states are unkown. In this paper, we derive explicit

expression for Bures geometric quantum discord and classical correlation,

together with all closest zero-discord states and closest product state for a

five-parameter family of states. For general X-states, a seven-parameter family

of that have been of interest in a variety of contexts in the field, we not

only calculate the Bures geometric quantum discord for a wide class of this

kind of states, but also provide a analytic upper bound for entirety.