  We study quantum discord between two free modes of a massive scalar field in
a maximally entangled state in de Sitter space. We introduce two observers, one
in a global chart and the other in an open chart of de Sitter space, and the
observers determine the quantum discord created by each detecting one of the
modes. This situation is analogous to the relationship between an observer in a
Minkowski chart and another in one of the two Rindler charts in flat space. We
find that the state becomes less entangled as the curvature of the open chart
gets larger. In particular, for the cases of a massless, and a conformally
coupled scalar field, the entanglement vanishes in the limit of infinite
curvature. However, we find that the quantum discord never disappears even in
the limit that entanglement disappears.
