Entropic Uncertainty Relation for Dirac Particles in Garfinkle-Horowitz-Strominger Dilation Space-Time

The quantum-memory-assisted entropic uncertainty relation for Dirac particles in the background of a Garfinkle-Horowitz-Strominger (GHS) dilation black hole is investigated, and the relationship between the entropy uncertainty and the quantum entanglement of a hybrid qubit-qutrit state in the GHS space-time analyzed. The results show that the physically accessible uncertainty increases while the inaccessible uncertainty decreases as the dilation parameter of the black hole enhances. Moreover, the evolution behavior of the uncertainty is inversely correlated with that of the entanglement between the quantum memory and the particle to be measured. Meanwhile, a method to steer the entropic uncertainty with the technique of weak measurement reversal is proposed. It is found that the uncertainty can be reduced effectively by adjusting the appropriate measurement strength. These findings may lead to a deeper understanding of entropy uncertainty dynamics, as well as its steering in a curved space-time.