Relationship between first-order coherence and the maximum violation of the three-setting linear steering inequality for a two-qubit system

Coherence and nonlocal correlations are two fundamental features of quantum mechanics and the relations between them have received much attention recently. While the relations of coherence to Bell nonlocality and to entanglement have been established, an interesting question left open is how to quantitatively characterize the relation of coherence to steering, which is one kind of nonlocal correlation lying between Bell nonlocality and entanglement. In this paper, we address this question by considering the first-order coherence and the three-setting linear steering inequality for a two-qubit system. Interestingly, we find that the first-order coherence for both subsystems has a complementary relation with the maximum violation of the three-setting linear steering inequality. A weighted sum of their squares keeps invariant under unitary operations, although each of them changes in general. This suggests that the maximum violation of the three-setting linear steering inequality can be taken as a measure of hidden coherence unveiled by unitary operations.