Measurement Uncertainty and Its Connection to Quantum Coherence in an Inertial Unruh-DeWitt Detector

The dynamic characteristics of measured uncertainty and quantum coherence are explored for an inertial Unruh-DeWitt detector model in an expanding de Sitter space. Using the entropic uncertainty relation, the uncertainty of interest is correlated with the evolving timet, the energy level spacing delta, and the Hubble parameterH. The investigation shows that, for short time, a strong energy level spacing and small Hubble parameter can result in a relatively small uncertainty. The evolution of quantum coherence versus the evolving time and Hubble parameter, which varies almost inversely to that of the uncertainty, is then discussed, and the relationship between uncertainty and the coherence is explicitly derived. With respect to thel(1)norm of coherence, it is found that the environment for the quantum system considered possesses a strong non-Markovian property. The dynamic behavior of coherence non-monotonously decreases with the growth of evolving time. The dynamic features of uncertainty and coherence in the expanding space with those in flat space are also compared. Furthermore, quantum weak measurement is utilized to effectively reduce the magnitude of uncertainty, which offers realistic and important support for quantum precision measurements during the undertaking of quantum tasks.