We calculate the quantum discord between two free modes of a scalar field
which start in a maximally entangled state and then undergo a relative,
constant acceleration. In a regime where there is no distillable entanglement
due to the Unruh effect, we show that there is a finite amount of quantum
discord, which is a measure of purely quantum correlations in a state, over and
above quantum entanglement. Even in the limit of infinite acceleration of the
observer detecting one of the modes, we provide evidence for a non-zero amount
of purely quantum correlations, which might be exploited to gain non-trivial
quantum advantages.Comment: 4 pages, 2 figure