Uncertainty relations for quantum coherence in the background of dilaton black holes

The coherence of a quantum system can be considered as the available physical resource, and its quantification respects the choice of reference bases. In this paper, we propose the uncertainty relations for quantum coherence (URQC) of a bipartite system AB in mutually unbiased bases, where particle A is the measured particle and B is regarded as the quantum memory. It is confirmed that the Holevo quantity can improve the lower bound of coherence. By defining the tightness as the difference between coherence and its lower bound, we find that the tightness of the improved URQC is independent of the quantum memory. As an example of application, we investigate the URQC of Dirac particles in the background of a Garfinkle–Horowitz–Strominger dilaton black hole beyond the single-mode approximation. It shows that the lower bound of coherence decreases monotonically with the increase of dilaton parameter due to the Hawking effect. Moreover, since the subsystem A is not affected by the black hole, the tightness of the improved URQC is always keep constant. It worth mentioning that the change of coherence can be precisely predicted via the known tightness and the improved lower bound measured experimentally. (letter)