Exploration of entropic uncertainty relation for two accelerating atoms immersed in a bath of electromagnetic field

The uncertainty principle as an elementary theory of quantum mechanics plays an important role in quantum information science. In this paper, we study the dynamics of quantum-memory-assisted entropic uncertainty relation for two accelerating atoms coupled with a bath of fluctuating electromagnetic field. The master equation that the system evolution obeys is firstly derived. We find that the mixedness is bound up with the entropic uncertainty. For equilibrium state, the tightness of uncertainty vanishes. For the initial maximum entangled state, the tightness of uncertainty experiences a slight increase and then declines to zero with evolution time. It is found that the greater acceleration makes the uncertainty faster reach a maximum value and stable value. For a fixed acceleration, the uncertainty with different two-atom separations converges to a fixed value. Furthermore, we utilize weak measurement reversal to manipulate the entropic uncertainty. Our explorations may suggest a method of probing entanglement, acceleration effect and vacuum fluctuation effect with entropic uncertainty.