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.

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