Dynamical Measurement's Uncertainty in the Curved Space-Time

The dynamical characteristics of measurement's uncertainty are investigated under two modes of Dirac field in the Garfinkle-Horowitz-Strominger dilation space-time. It shows that the Hawking effect induced by the thermal field would result in an expansion of the entropic uncertainty with increasing dilation-parameter value, as the systemic quantum coherence reduces, reflecting that the Hawking effect could undermine the systemic coherence. Meanwhile, the intrinsic relationship between the uncertainty and quantum coherence is obtained, and it is revealed that the uncertainty's bound is anti-correlated with the system's quantum coherence. Furthermore, it is illustrated that the systemic mixedness is correlated with the uncertainty to a large extent. Via the information flow theory, various correlations including quantum and classical aspects, which can be used to form a physical explanation on the relationship between the uncertainty and quantum coherence, are also analyzed. Additionally, this investigation is extended to the case of multi-component measurement, and the applications of the entropic uncertainty relation are illustrated on entanglement criterion and quantum channel capacity. Lastly, it is declared that the measurement uncertainty can be quantitatively suppressed through optimal quantum weak measurement. These investigations might pave an avenue to understand the measurement's uncertainty in the curved space-time.