  Heisenberg's uncertainty principle is a fundamental element in quantum
mechanics. It sets a bound on our ability to predict the measurement outcomes
of two incompatible observables simultaneously. In quantum information theory,
the uncertainty principle can be expressed using entropic measures. The
entropic uncertainty relation can be improved by considering an additional
particle as a memory particle. The presence of quantum correlation between the
memory particle and the measured particle reduces the uncertainty. In a curved
space-time, the presence of the Hawking radiation can reduce quantum
correlation. Therefore, concerning the relationship between the quantum
correlation and entropic uncertainty lower bound, we expect that the Hawking
radiation increases the entropic uncertainty lower bound. In this work, we
investigate the entropic uncertainty relation in Garfinkle-Horowitz-Strominger
(GHS) dilation black hole. We consider a model in which the memory particle is
located near the event horizon outside the black hole, while the measured
particle is free falling. To study the proposed model, we will consider
examples with Dirac fields. We also explore the effect of the Hawking radiation
on the quantum secret key rate.
